(4) Said retirement board shall, upon notification of the death of a member or surviving spouse covered under the provisions of this section, notify the treasurer of the governmental unit of the death of said member or surviving spouse. Upon receipt of such notification, the treasurer shall discontinue said member or surviving spouse's coverage under the group policy in effect for said governmental unit unless said member is survived by a spouse who remains eligible for continued coverage in which case said retirement board shall continue withholding in accordance with the provisions of this section. In the event that said policy entitled the member to life insurance benefits, said benefits shall be paid in accordance with the terms of the policy; provided, however, that the treasurer of the governmental unit shall notify said retirement board of the death of the member or surviving spouse at the same time or prior to the notification of the group life insurance carrier of such death.