Is it permissible for the husband to back out of his prior agreement with his wife and her mother that the apartment be shared equally between them, and insist that the apartment be registered solely in his name, justifying this by applying Islamic law and his eagerness for his sisters' inheritance, and refusing to register it in their daughter's name?

If the agreement is on an unspecified, unassigned apartment as a mahr (dowry), this is invalid according to the majority of scholars due to the ambiguity (al-jahalah). In this case, the wife is entitled to a mahr al-mithl (a dowry equivalent to that of women of her status), provided it is not less than the known, named mahr. The husband is not obliged to register an apartment in the wife's name.