Is it permissible for a third party to pay off another person's debt while receiving the discount offered by the shop owner for cash payment? And what is the Sharia ruling on this issue?

This transaction is the sale of a deferred debt for a lesser immediate cash amount of the same kind. It combines riba al-fadl (usury of surplus) and riba al-nasi'a (usury of delay), thus it is Islamically prohibited.

The Islamic Fiqh Academy has clarified that discounting commercial papers is not permissible Islamically because it leads to the forbidden riba al-nasi'a.

The Sharia-compliant alternative for this transaction is for the third party (financier) to sell actual goods to the shop owner (creditor) for a price equal to the debt owed by the customer (debtor) to the shop owner. Then, the financier accepts the shop owner's hawala (transfer of debt) on the customer. The financier can then sell the goods at a higher price to gain profit.

Scholars have agreed on the impermissibility of securitizing deferred monetary debt and trading it in a secondary market, whether it is sold for an immediate cash payment of the same kind (discounting bills of exchange) or of a different kind, due to its involvement with riba.