Subject to §B, below, when a unit of State government seeks reimbursement from the State Insurance Trust Fund for an occurrence of loss, damage, or liability, the unit shall file its claim with the Treasurer within 60 days after the unit discovers the loss, damage, or liability. If the unit discovers an occurrence of loss, damage, or liability in June, it shall file its claim for reimbursement with the Treasurer before July 20th of the next fiscal year.