What is the ruling on a murabaha transaction offered by a riba-based bank to Muslim customers in the United States, where the customer chooses the house and negotiates its price, then the bank buys the house and sells it to the customer in installments with an added profit, knowing that the customer is not obligated to buy after the bank's promise to him, and that the two contracts are separate but are often signed on the same day?

The aforementioned transaction (Murabahah to a party ordering a purchase) is permissible if it fulfills its conditions, the most important of which is the bank's true ownership of the commodity before selling it to the customer.

The validity of the transaction is not affected by the party ordering the purchase bearing the expenses of research, evaluation, and inspection, or by reserving the house from its owner until the transaction with the bank is completed.

As for the fate of the reservation amount, it is not clear from the question whether it is refundable or becomes the property of the real estate owner. This requires further details to rule on it, but it does not affect the validity of the transaction with the bank.