Is it permissible for the owner of an exchange shop to give a sum in dollars to another shop so that it may purchase goods, and then the owner of that shop repays the sum in dollars after selling the goods and buying dollars from the same exchanger at the prevailing rate?

This transaction is forbidden and invalid because in reality, it is a loan that draws a benefit to the lender, making it usury (riba), which is prohibited by Islamic law. This includes combining a loan with a sale, due to the benefit the lender gains from the loan. Pawnbrokers and merchants must refrain from this forbidden transaction and strive for a goodly loan (qard hasan (definition)) or to earn profit through permissible means, such as partnership.