Tahleel marriage is haram and invalid
Question

My friend has divorced his wife the third and final divorce. Is it permissible that I marry her then divorce her so that she can return to her first husband?.
Praise be to Allah.If a man divorces his wife for the third time, then she is not permissible for him to marry until she has married another man, because Allah says (interpretation of the meaning): “And if he has divorced her (the third time), then she is not lawful unto him thereafter until she has married another husband” [al-Baqarah 2:230].
It is stipulated that this marriage which will make her permissible for her first husband should be a valid marriage. Temporary marriage (mut’ah marriage) or marriage for the purpose of making her permissible for her  first husband then divorcing her (tahleel marriage) are both haram and invalid according to the vast majority of scholars, and it does not make the woman permissible for her first husband.  
See: al-Mughni (10/49-55). 
There are saheeh ahaadeeth from the Prophet (peace and blessings of Allah be upon him) which show that tahleel marriage is haram. 
Abu Dawood (2076) narrated that the Prophet (peace and blessings of Allah be upon him) said: “Allah has cursed the muhallil and the muhallal lahu.” This was classed as saheeh by al-Albaani in Sunan Abi Dawood. 
The muhallil is the one who marries a woman and divorces her so that she can go back to her first husband, and the muhallal lahu is the first husband. 
Ibn Majaah (1936) narrated from ‘Uqbah ibn ‘Aamir (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “Shall I not tell you of a borrowed billy-goat.” They said, Yes, O Messenger of Allah. He said, “He is al-muhallil. May Allah curse al-muhallil and al-muhallal lahu.” Classed as hasan by al-Albaani in Saheeh Sunan Ibn Maajah. 
‘Abd al-Razzaaq (6/2650 narrated that ‘Umar ibn al-Khattaab (may Allah be pleased with him) said whilst addressing the people: “By Allah, no muhallil or muhallal lahu will be brought to me but I will stone them.” 
This applies whether he states his intention clearly when doing the marriage contract and they stipulate that when he has made her permissible for her first husband he will divorce her, or they do not stipulate that and he intends it to himself only. 
Al-Haakim narrated from Naafi’ that a man said to Ibn ‘Umar: I married a woman and made her permissible for her first husband, and he did not tell me to do that and he did not know. He said: No, marriage should be based on genuine intentions; if you like her then keep her, and if you do not like her then leave her. He said: At the time of the Messenger of Allah (peace and blessings of Allah be upon him) we would regard that as zina. And he said: They will still be adulterers, even if they remain for twenty years. 
Imam Ahmad was asked about a man who married a woman intending thereby in his heart to make her permissible for her first husband, but the woman did not know about that. He said: He is a muhallil, and if he intends thereby to make her permissible for her first husband, then he is cursed. 
Based on that, it is not permissible for you to marry this woman if you intend thereby to make her permissible for her first husband. Doing that is a major sin, and the marriage will not be valid, rather it is zina – Allah forbid.