I agree with Duchess, burn the darn card!!! Also, I'd explain to the cardholder that we have sufficient proof to know who is doing the fraudulent activity and that the Bank will be pressing charges against this individual.
And, as Randy stated in his earlier post, the card member should have received no benefit. If there's any indication he did, you may want to consider legal action against him for filing a false claim.
At the very least, I'd take away card privileges (and notate the account with some kind of WARNING message), but I'd be looking to close the account relationship altogether.