Interbank transfers, whether accomplished via physical check or electronic transfer, do not require an exchange of currency, just the exchange of liabilities (deposits).
Thanks Scot. Are you sure about that? I don’t see how it can make sense from an accounting point of view (deposits can’t just be striked-out by one bank and added to the balance sheet of the second bank). I believe the rest of your exposition (which I think is flawed) is connected to the above point, so maybe it would be helpful to sort it out first.