Can a financial institution prevent the posting of an Official Check that was originally purchased with fraudulent funds
from their customer's account.

In other words, another financial institution (BANK A) has a customer who had their computer system hacked. The perpetrators then open an account at Bank B, and the perpetrators subsequently initiate a wire transfer into their account at Bank B.
Bank B posts the wire. The perpetrators that hacked Bank A's customer withdraw the funds by Official Check before Bank B become aware that the account received a fraudulent wire transfer.. How can Bank B stop payment on the official check that was purchased with fraudulent wire fund? It's my understanding that Stop Payments can not be placed on an Official Check so how does Bank B prevent the Official Check from posting? Can a Stop Payment be placed in situations of this type when an Official Check as purchased using fraudulent funds?

You can't. The Uniform Commercial Code will place liability on your bank for returning its own cashier's check as a stop payment. The legitimate party that gives value for the bad guys negotiating the cashier's check cannot be on the short end of this stick. This is between Bank A and it's customer as to who bears the loss. You do not have a dog in this fight and I don't advice sticking my hand in between the two and risk getting bit, yourself.