Is it permissible for the wife to marry another man after leaving her home as a result of her husband's oath to divorce her thrice should she leave, knowing that there are no official documents proving the marriage and that the husband wishes to reconcile while she does not?

If a man tells his wife: "If you leave the apartment, you are divorced with three pronouncements," and she then leaves, the majority of scholars hold that the three divorces occur, and she becomes irrevocably separated from him, not becoming lawful for him again until she marries another husband willingly and he divorces her after consummating the marriage.

Shaykh al-Islam Ibn Taymiyyah is of the view that if the husband did not intend divorce but rather intended to prevent her from leaving, then divorce does not occur; instead, he owes an expiation for a broken oath.

Given the difference of opinion, it is best for the questioner to present the matter to the Sharia court. Not officially documenting the marriage does not prevent the occurrence of divorce if the pillars of a valid Sharia marriage are present, namely a guardian, two just witnesses, and a صيغة (formulation of offer and acceptance).