Is it permissible to claim a debt that the father waived for his daughter's husband, and if it is permissible to claim it, is this money considered an inheritance or a gift divided among the daughters?

When a debt is established in the debtor's liability, their liability is not cleared except by the extinguishment of the debt through release (ibra'). Release is effected by an offer from the creditor and does not require acceptance from the debtor, but it is rejected by their refusal. This is because release is both a waiver (isqat) and a transfer of ownership (tamleek). From the perspective of waiver, it does not depend on acceptance; from the perspective of transfer of ownership, it is rejected by refusal. Since the debtor here accepted the release during the creditor's lifetime, the money is no longer considered a debt owed by him nor part of his father-in-law's estate. If the husband wishes to compensate the creditor's heirs, he may donate some money to them without being obligated to distribute it equally among the heirs or adhere to their shares of inheritance.