It is hard for him to go to work so he signs in as present on the days when he is absent
Question

                I decided to take early retirement and move to the city where my family and my wife’s family live because my wife’s mother is very sick and needs to have her daughter close by. 

So I rented an apartment in that city and moved my furniture there. 

I submitted a letter of resignation to my work, but the boss advised me to delay it a little because they were going to open a branch in the city to which I was moving, or they were thinking of offering compensation to those who wanted to retire. For two months I have only been in to work a few times, and I sign for all the days on which I am absent from work.

 My question is: is my situation and my absence from work right or not? If it is not right, what is the ruling on the past days when I signed but was not present? Should I give my salary for those two months to the administration to spend on the department, so they can buy office supplies or computer equipment that the department needs? Or should I give it in charity? What is the ruling? Or should I carry on going two days a week and signing for the other days?.
Praise be to Allah.
    Firstly: 

    We ask Allaah to reward you with good for your desire to 
    treat your wife’s mother kindly and to bring your wife close to her family, 
    and for the travelling, moving and giving up work that you are putting up 
    with for this purpose. 

    Secondly: 

    What you have done – signing for the days when you are absent 
    from work – is undoubtedly a haraam action, because it involves lying and 
    consuming people’s wealth unlawfully. Allaah says (interpretation of the 
    meaning): 

    “O you who believe! Eat not up your property among 
    yourselves unjustly”

    [al-Nisa’ 4:29]

    And the Prophet  (peace and blessings of Allaah be upon 
    him) said: “Truthfulness leads to righteousness and righteousness leads to 
    Paradise. A man will keep speaking the truth and striving to speak the truth 
    until he will be recorded with Allaah as a siddeeq (speaker of the 
    truth). Lying leads to immorality and immorality leads to Hellfire. A man 
    will keep telling lies and striving to tell lies until he is recorded with 
    Allaah as a liar.” Narrated by al-Bukhaari, 5629; Muslim, 4719. 

    Thirdly: 

    The salary that you have taken in return for these days 
    should be given back to your workplace; it is not permissible for you to 
    keep it because it is haraam wealth. The Prophet  (peace and blessings 
    of Allaah be upon him) said: “Every body that is nourished with haraam food, 
    the Fire is more fitting for it.” Narrated by al-Tabaraani from Abu Bakr; 
    classed as saheeh by al-Albaani in Saheeh al-Jaami, 4519. 

    Al-Tirmidhi (614) narrated from the hadeeth of Ka’b ibn 
    ‘Ajzah: “There is no flesh that grows from haraam food but the Fire is most 
    suited for it.” Classed as saheeh by al-Albaani in Saheeh al-Tirmidhi. 
You have no right to 
    give this money in charity, because wealth can only be given in charity when 
    its owner is unknown or it is too difficult to reach him. 

    Fourthly: 

    It is not permissible for you to carry on being absent from 
    work whilst signing in as present. You should look for a way out that will 
    not involve sin, or you should agree to take early retirement now, without 
    getting the incentive of the lump sum that you mentioned. Remember that that 
    which is with Allaah can only be attained by obeying Him, and that haraam 
    wealth erases blessings and will bring evil consqeuences in this world and 
    in the Hereafter. 

    This advice was offered by Shaykh Ibn Baaz (may Allaah have 
    mercy on him) to the one who was careless about his attendance at work, and 
    was not honest in recording the times when he was present. He (may Allaah 
    have mercy on him) said: “It is a duty for every Muslim to fulfil his trusts 
    and to beware of cheating at work with regard to attendance and absence and 
    in all matters. What he must do is to record the time when he entered and 
    the time when he left, so that he will have discharged his duty. The boss 
    has to advise them sincerely and direct them to do that which is good, and 
    warn them against cheating. And Allaah is the Source of strength. End quote 
    from Majmoo’ Fataawa al-Shaykh Ibn Baaz, 19/356. 

    We ask Allaah to guide us and you. 

    And Allaah knows best.