Is it permissible in Sharia for one person to borrow from an Islamic bank on behalf of another, with the latter agreeing to repay the installments and give him a reward in return for his favor?

What you promised him as a payment in exchange for that transaction is considered usurious interest, because he loaned you the amount he obtained in his name from the bank, and you will repay him the loan and give him an increase in return. Every loan that draws a benefit is usury (riba). The Sharia has prohibited every loan that brings a benefit to the lender, based on the Prophet's (peace be upon him) saying: "Every loan that draws a benefit is usury." Although Al-Albani deemed it weak, scholars have adopted it. Ibn Abd al-Barr says: "Every increase in a loan, or benefit that the lender gains, is usury, even if it were a handful of fodder, and that is forbidden if it is stipulated."