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If the third divorce took place as a proper pronouncement of “divorce” and without compensation, then the woman will be absolutely and irrevocably divorced, and she will never be lawful again for her former husband unless she marries another man and gets divorced from him, even if the third divorce took place upon the wife’s request.

However, if the separation in this third instance took place in lieu of compensation, then it is deemed to be a revocation of the marriage and not a divorce. Therefore, the two of them are free to get remarried if that is what they wish to do.

Ibn `Abbâs said: “Khul` is a separation and not a divorce” [Related by Ahmad. Ibn Hajr said: "Its line of transmission is authentic." al-Talkhîs al-Habîr (3/231)].

Someone asked Ibn `Abbâs about a man who divorced his wife twice, then she made khul` with him; can he marry her again? Ibn `Abbâs replied: “Yes, Allah mentions divorce at the beginning and at the end of the verse and mentions khul` in between.” [Related by `Abd al-Razzâq (11771)].

Ibn al-Qayyim said: "This is the school of thought of Ibn `Abbâs, `Uthmân, Ibn `Umar, al-Rubayyi` and her uncle. In fact, it was never related by any Companion that khul` is a divorce." [Zâd al-Ma`âd (5/197)].

Ibn Khuzaymah said: “It was never established that khul` is a divorce [al-Talkhîs al-Habîr (3/231)].

This is the opinion of Ibn Taymiyah. He gives strong support for this opinion in Majmû` al-Fatâwa (32/289).

And Allah knows best.

Source: Islam Today