We have a consumer who disputed a transaction and after we completed the investigation and sent the final disposition notice (an error did occur) the consumer called and said that he did authorized the transaction. Can we debit the provisional credit that we provided the consumer since he did authorize the transaction even though the investigation has been finalized??

Why not? You now have information that it was in fact, authorized!

I concur, the customer is granting you permission to reverse the "final" credit.

What you cannot do is reverse final credit if you have determined that the transaction was authorized after finalizing your investigation and your customer still insists that the transaction is unauthorized. In this case, it would be a violation to reverse final credit without your customer's consent.