Should the payment of the deceased father's debt be prioritized over the completion of the wife's dowry, knowing that neither the debt nor the dowry is being claimed by anyone?

If your father gave you a sum of money as a debt, it remains, as per its original nature, a debt owed to the heirs after his death, and you must inform them about it. If you are unable to repay it, you must write a will concerning it. As for a gift (hiba), it is not permissible to make it conditional. If your wife's dower (mahr) is not yet due, the debt to the heirs takes precedence over it. If her dower is immediately due and the money is insufficient to cover everyone's right, then pro-rata distribution can be applied among everyone, where the money is divided among them in proportion to their debts.