During July, annually, the Secretary shall compile a list of all securities on deposit, pursuant to this Article, for more than 3 years and concerning which he has received no notice as to the pendency of any judicial proceeding that could affect the disposition thereof. Thereupon, he shall promptly send a notice to the last known address of each depositor advising him that his deposit will be subject to escheat to the State of Illinois if not claimed within 30 days after the mailing date of such notice. At the expiration of such time, the Secretary of State shall file with the State Treasurer an order directing the transfer of such deposit to the general revenue fund in the State Treasury. Upon receipt of such order, the State Treasurer shall make such transfer, after converting to cash any other type of security. Thereafter any person having a legal claim against such deposit may enforce it by appropriate proceedings in the Court of Claims subject to the limitations prescribed for such Court. At the expiration of such limitation period such deposit shall escheat to the State of Illinois.