Is the aforementioned transaction, which involves paying a sum for registration and receiving a receipt for a greater value to purchase from specific stores, or paying half the price of a commodity to obtain it later, permissible in Islamic law?

The aforementioned transaction is forbidden because it is a loan that yields a benefit, and every loan that yields a benefit is usury (riba). The loan here is from the office to the customer, and the benefit is the discount, which is obtained through collusion between the parties. This loan is based on exploiting people's money in exchange for discounts from certain stores. Scholars have unanimously agreed on the prohibition of every loan that yields a benefit, whether the one offering the benefit is the borrower or an external party. The office is considered to be consuming usury, and the borrower is assisting in it. Furthermore, this office may be an agent for the store, which would make the loan clearly usurious.