If we fire dishonest employee, can he collect unemployment comp and vacation pay?

Q. We have an employee who recently submitted an expense report for more than $1,300 for an extended business trip. We accidentally reimbursed him twice. He did not report the double payment and we did not learn of the mistake until an internal audit two months later. Our company policy prohibits dishonesty and we want to fire the worker for violating this rule. Will he be able to collect unemployment benefits? May we withhold the vacation pay that is due to him under our policy, which would just about make us whole?