Is it permissible to deal with an interest-based bank that sells property to a client after acquiring it, with the client acting as an undisclosed agent for the bank in purchasing the property, and the client committing to buy the property from the bank after the bank has purchased it?

The scenario mentioned in the question—Murabaha to the one who promises to buy—is permissible according to the majority of contemporary scholars, under specific conditions. There appears to be no Sharia-related impediment to the bank appointing the buyer as an agent and the latter committing to the purchase order. However, if banks stipulate interest or late fees for delayed installment payments, this constitutes a prohibited usurious transaction, rendering the dealing impermissible.