Access to the box varies state to state and even bank to bank.One big question. Was income tax paid on the winnings? If not, pay the tax and open a bank account in the name of his newly created trust. Assets owned by a trust are exempt from probate (and judges). He can make whatever provision for the girl that he desires.
A big problem seems to be who would he name as trustee after himself. If family and friends are not trustworthy, his attorney or the bank can be named. Fees for either would be high.

If taxes were paid there is no problem removing the cash from the box and putting it in a bank.