Customer A placed a stop payment order (check) with the bank.
Customer B, also a bank customer, presents the check for payment over the counter for cash, and teller pays the item not recognizing the stop payment order in place.
Bank later identifies the error and confirms with Customer A that the stop payment order is still valid. Bank honors the stop payment order.

Is chargeback allowable to Customer B or does Bank take the loss because of the error?

Since you actually cashed the check, that represents final payment.

Thank you.

Under UCC 4-407, the bank that pays a check over a stop payment order is subrogated to the rights:

(1) Of any holder in due course on the item against the drawer or maker;

(2) Of the payee or any other holder of the item against the drawer or maker either on the item or under transaction out of which the item arose; and

(3) Of the drawer or maker against the payee or any other holder of the item with respect to the transaction of which the item arose.

So, if your customer had a claim against the payee to recover payment had the payment not been stopped, you now stand in the legal position your customer would have been in and can attempt to recover the payment to Customer B. But you can't do it via a charge-back. If the dollar amount is sufficient to warrant it, discuss the problem with bank counsel.