Section 13A. Upon written request of the department, there shall be paid out of the state treasury, from such funds as may be available therefor, to any person determined by the attorney general to be entitled to compensation for damage to his property caused by the act of any inmate of the Lyman school for boys at Westborough, the industrial school for girls at Lancaster, the industrial school for boys at Shirley, the department of youth services reception center at Westborough or any other institution of which the department has management, government and care under the provisions of section two while escaping therefrom, such sum as the attorney general shall determine to be just and reasonable and as the governor and council shall approve; provided, that written notice of said damage and claim for compensation therefor be filed with the department within one year next after the date on which such damage occurred.