Is it permissible for the bank to appoint me as its agent to purchase shares that will eventually be owned by it, and then sell them to me on a murabaha basis, and is this considered a necessity to avoid others buying them or to avoid transfer of ownership costs?

The difference between the bank appointing a brokerage firm or other entity to purchase shares and deposit them into the portfolio of the buyer (the instructing party), and the bank appointing the buyer (the instructing party) himself. The principle is that the institution should purchase the commodity itself. It is permissible for it to appoint someone other than the buyer, but it should not appoint the client (the instructing party) unless there is an urgent need. An agent should not sell to himself. When appointing the client, the institution must pay the price directly to the seller and obtain documents to confirm the reality of the sale. If there is an urgent need for the bank to appoint you to purchase shares, there is no harm, provided that the aforementioned controls are adhered to. Otherwise, it is better to avoid it to escape the suspicion of fictitiousness.