The State Treasurer shall not pay any warrant which is presented to him or her for payment more than two years after the date of its issuance if issued prior to October 1, 1992, or one year after the date of its issuance if issued on or after October 1, 1992, and any such warrant shall cease to be an obligation of the State of Nebraska and shall be charged off upon the books of the State Treasurer. Except as otherwise provided by law, the amount stated on such warrant shall be credited to the General Fund. Such warrant may, however, thereafter be presented to the State Claims Board which may approve a claim pursuant to the State Miscellaneous Claims Act for the amount of the warrant.