Where money in an individual person’s account on the books of the Hawaii youth correctional facilities has not been claimed by such person or the person’s legal representative within one year after the person has or would have reached the age of majority, the director shall remit to the director of finance all moneys standing to the credit of the person in the account, taking the receipt of the director of finance therefor. All such moneys shall thereupon, become a state realization; provided that at any such time within five years after the payment into the treasury of moneys from any such account, the person or the legal representative of the person, who would have been entitled to receive the same from the director upon making satisfactory proof to the comptroller of the State of such right, shall receive the amount thereof out of any moneys not otherwise appropriated upon warrant drawn by the comptroller.