Collections between customers of the same bank are very easy, considering that they require no interaction between different banks. All liability would fall on the single bank in question, as in such banking practices, the payor and depository bank would be the same, and therefore, the bank would have no other bank to assume liability.
The financial institution in question would process a check from one of its customers to another in much the same way as it might process any check, except that the bank can instantly extend additional “credit” to the payee’s account so as to reflect the additional funds being deposited, while subtracting credit from the drawer’s account. This credit which the bank first extends to the payee’s account might be provisional at first, but the rules for making funds available describe this situation specifically.
The bank would have until the beginning of the second business day after the deposit of the check to dishonor it, and if it did not do so by then, then the provisional credit which it extended to the payee would become officially finalized. The banking term for a check that is payable from one customer of a bank to another is an “on-us item”, or a house check.