Families of Fallen Servicemembers First Act This bill provides a permanent appropriation for the payment of death gratuities and related benefits to survivors of deceased members of the uniformed services during a period of lapsed appropriations. The bill provides the appropriations at the rate and under the conditions provided for the most recent fiscal year for which an Act making appropriations for the uniformed services has been enacted. The appropriations are provided during a period of lapsed appropriations, in which appropriations are unavailable due to the absence of the timely enactment of an Act or joint resolution providing appropriations or continuing appropriations for the death gratuity and related benefits.