Are the heirs of the husband entitled to claim back the house that he sold to his wife during his lifetime, given that the sale and purchase were documented and ownership was transferred in her name, and there is an unauthenticated written waiver of the house?

The separation of a husband from his wife in exchange for compensation paid by the wife to him is called khulʿ, and the husband is entitled to the compensation his wife offered him. Khulʿ is concluded by offer and acceptance, and its documentation is not a condition for its validity. Khulʿ is not invalidated if the wife does not hand over the agreed-upon compensation; rather, it remains a debt owed by her. If the husband divorced his wife in exchange for her relinquishment of the house, and she relinquished it to him, then the house becomes the husband's right, and it must be given to his heirs after his death, because it became the property of their inheritor by virtue of the khulʿ contract.