Is it permissible to give zakat to pay off a debt on behalf of an imprisoned person, or for the creditor to deduct his debt from zakat money?

It is permissible to disburse Zakat to the debtor to settle his debt, because he is among the gharimin (those in debt). As for giving Zakat to the creditor, if it is with the debtor's permission, there is no problem. But if it is without his permission, it is a matter of dispute: The Hanafis and Shafi'is hold that it is not valid, while the Hanbalis consider it valid. The more cautious approach is to inform the debtor and seek his permission, or to hand him the money so he can pay off his debt himself.