He divorced her in return for half of the mahr after he accused her. Does he have the right to this money?
Question

                I am a religiously-committed young woman, praise be to Allaah. There was a problem between me and my husband – from whom I have a daughter –as the result of which I went to my father’s house. He had doubts about me and accused me with regard to my honour without any convincing reason, then he apologized, then he accused me again. That happened several times, which made me certain that he was afflicted with waswaas (whispers from the shaytaan). I could no longer bear it, so I went to my family. After I went to them, I stayed with them for four months, during which my husband only became more stubborn and insistent upon his position, without any proof or evidence against me. After that my brother went to him to try to work things out, but he insisted on his position, and asked me to repent, and the matter got worse. He spoke ill of my father and how he had raised me. At that point my brother and my father 
insisted that he should divorce me, otherwise they would refer our problem to the courts, and he would have to prove his accusations against me. My husband asked for half of the mahr in return for divorcing me, but after a while he divorced me without us giving him anything, and he kept quiet about that, and did not ask for the money again. 

Now Allaah has compensated me with another husband who is religiously committed, praise be to Allaah. My second husband has pointed out to me that I may owe some money to my first husband. Because I am afraid of doing something haraam and consuming people’s wealth and taking away their rights, I hope that you can advise me with regard to this matter. Please note that I do not have this money, and I do not ask him for any expenses for his daughter, but he sends some to her sometimes, and sometimes he does not send her anything. Does he have any right to my wealth? 

May Allaah reward you with good.
Praise be to Allah.For a 
    husband to slander his wife and accuse her with regard to her honour is a 
    major sin, which incurs a hadd punishment and means that his testimony is to 
    be rejected. He has to bring shar’i evidence to prove the accusation, or 
    else engage in li’aan. 
Ibn Qudaamah 
    (may Allaah have mercy on him) said:  
If he 
    slanders his chaste wife then he is subject to the hadd punishment, and he 
    is ruled to be a faasiq (evildoer) whose testimony is to be rejected, unless 
    he brings proof or engages in li’aan. If he does not bring four witnesses or 
    he refuses to engage in li’aan, then all of that applies to him. This is the 
    view of Maalik and al-Shaafa’i. 
This is 
    indicated by the verse in which Allaah, may He be exalted, says 
    (interpretation of the meaning): 
“And 
    those who accuse chaste women, and produce not four witnesses, flog them 
    with eighty stripes, and reject their testimony forever. They indeed are the 
    Faasiqoon (liars, rebellious, disobedient to Allaah)”
[al-Noor 
    24:4]
This is 
    general in meaning and applies to the husband and others. With regard to the 
    husband in particular, his li’aan may take the place of testimony in order 
    to cancel out the hadd punishment, judgement of being a faasiq and rejection 
    of his testimony. 
Also, the 
    Prophet  (peace and blessings of Allaah be upon him) said: “(Bring) 
    proof, or else the hadd punishment will be on your back.” And he said when 
    he conducted the process of li’aan: “The punishment in this world is easier 
    to bear than punishment in the Hereafter.” 
 Because he 
    has slandered (his wife), the hadd punishment should be carried out on him 
    if he admits to lying; therefore the hadd punishment is due unless he brings 
    the proof required by sharee’ah, as is the case with any other man.  
Al-Mughni 
    (9/30). 
Based on 
    this, what the husband must do is fear Allaah with regard to himself and his 
    wife, and he should refrain from bad talk. Speaking against his wife is an 
    attack on his own honour. He must also declare himself to be a liar by 
    asserting his wife’s innocence of what he has fabricated against her. If he 
    does not do that, then he deserves what Allaah has decreed for those who do 
    that, namely the hadd punishment, rejection of his testimony and being 
    judged to be a faasiq, and she has the right to demand that he divorce her, 
    and he should give her her rights in full. 
Secondly: 
Putting 
    pressure on one's wife by making false accusations, annoying her and beating 
    her in order to make her give up her mahr or any part of it is called 
    al-‘adl (treating the wife harshly in order to take away the dowry or part 
    of it), and it is haraam, unless she has committed blatant immorality. If 
    the husband does that, he has no right to what his wife has given up, and he 
    has to return it to her. If he refuses to divorce her, then she has the 
    right to free herself from him and give up her mahr or more or less than 
    that. If he is lying and is wronging her, then what he takes is evil and 
    haraam, and if he is telling the truth then what he takes is permissible for 
    him, so long as he has proven that which incurs the hadd punishment by means 
    of four witnesses or li’aan. This applies if he has accused her openly; 
    however, if he saw her commit an immoral deed and it is between him and his 
    Lord, then he may put pressure on her so that she may give up part of her 
    mahr in return for divorce. 
Shaykh 
    al-Islam Ibn Taymiyah (may Allaah have mercy on him) was asked about a man 
    who accused his wife of immorality; he did not see her do anything that is 
    disapproved of in sharee’ah, but he claimed that he sent her to a wedding 
    then he spied on her and did not find her at the wedding, but she denied 
    that. Then he went to her guardians and told them what had happened, and 
    they called her to respond to what her husband was saying, but she refused 
    for fear of being beaten, and she went out to the house of her maternal 
    uncle. Then after that the husband used this incident to deny her her rights 
    and he claimed that she had gone out without his permission. Does that 
    invalidate her rights, and should her denial be accepted? 
He replied: 
Allaah, may 
    He be exalted, says (interpretation of the meaning): 
“O you 
    who believe! You are forbidden to inherit women against their will; and you 
    should not treat them with harshness, that you may take away part of the 
    Mahr you have given them, unless they commit open illegal sexual 
    intercourse”
[al-Nisa’ 
    4:19]
So it is not 
    permissible for a man to force his wife by putting pressure on her to make 
    her give up part of the dowry, or to beat her for that purpose. But if she 
    commits open illegal sexual intercourse then he has the right to put 
    pressure on her to give up all or part of the dowry in return for divorce. 
    This is with regard to that which is between a man and Allaah. 
As for the 
    family of the woman, they should find out the truth and help to establish 
    it. If they find out that she is the one who has transgressed the sacred 
    limits of Allaah and betrayed her husband, then she is the wrongdoer and 
    transgressor and she should give up the dowry in return for divorce. If he 
    says that he sent her to a wedding and she did not go to the wedding, then 
    he should ask her where she went. If he is told that she went to some people 
    about whom there is no suspicion, and those people confirm what she says, 
    all well and good; if they say that she did not come to them and she did not 
    go to the wedding, then there is something dubious and this supports what 
    the husband is saying. 
As for the 
    furniture etc that she brought from her father’s house, he should give it 
    back to her whatever the case, but if they reconcile then reconciliation is 
    good. 
If the woman 
    repents, then it is permissible for her husband to keep her and there is 
    nothing wrong with that, for the one who repents from sin is like one who 
    did not sin at all. 
If they do 
    not agree for her to go back, then she can give up the dowry and the husband 
    can let her go (khula’), because khula’ is permissible according to the Book 
    of Allaah and the Sunnah of His Messenger, as Allaah says (interpretation of 
    the meaning): 
“Then if 
    you fear that they would not be able to keep the limits ordained by Allaah, 
    then there is no sin on either of them if she gives back (the Mahr or a part 
    of it) for her Al-Khul‘ (divorce)”

    [al-Baqarah 2:229]
Majmoo’ 
    al-Fataawa (32/283, 284) 
Thirdly: 
It seems to 
    us that you owe him nothing, and that what he is demanding of half of the 
    mahr is not his right according to sharee’ah. It seems that he has had 
    second thoughts or that someone has told him about the ruling, so he did not 
    persist in his demands. He may have given up half of the mahr in return for 
    your looking after his daughter and spending on her. 
Whatever the 
    case, he has not produced witnesses for what he has accused you of, and he 
    has not engaged in li’aan, and he has not seen anything that would make him 
    not a sinner between him and his Lord. All of this means that you are in the 
    right and he is not – according to what is said in your question – so he has 
    no right to stipulate that he be given half of the mahr. 
May Allaah 
    bless your new husband for you, whom Allaah has granted to you, and may He 
    reward him with good for telling you to ask about the rights of your first 
    husband. This is indicative of a good character and great religious 
    commitment. 
We ask 
    Allaah to grant him the best of rewards and to make him a good compensation 
    for you and your daughter, and to bring you together in goodness and bless 
    you with goodly offspring. 
We ask 
    Allaah to guide your first husband to repent sincerely and to heal him if he 
    is sick, and to compensate him with something better. 
And Allaah 
    knows best.