Is it permissible for a bank to purchase air conditioners for a certain price and sell them to a client at a higher price, with the client not taking possession of the air conditioners but instead receiving the amount in cash, under the pretext that the bank purchased and sold the air conditioners? What is the ruling if it is usury?

Judging something requires knowledge of its conditions and how it is done. If the bank obligated the brother to handle the transaction and not to receive the devices or dispose of them except through the bank, then the transaction is forbidden. One can refer to the scholars who permitted the transaction. However, if the transaction was forbidden and it was completed, and the brother was unaware of its prohibition, then he must seek forgiveness and resolve not to return to such a thing, as Allah says: "So whoever receives an admonition from his Lord and desists, he shall be pardoned for what is past." The transaction of buying air conditioners is not usurious, but if the bank handles the entire transaction, from taking possession of the goods and selling them on behalf of the purchaser, or if this is stipulated explicitly or by custom, then it becomes forbidden, similar to organized tawarruq.