Fry Scholarship Improvement Act of 2019 This bill expands eligibility for the Marine Gunnery Sergeant John David Fry Scholarship, commonly referred to as the Fry Scholarship, which entitles specified dependents of an active-duty servicemember who died in the line of duty on or after September 11, 2001, to educational assistance under the Post-9/11 GI Bill. Specifically, the bill expands eligibility for the Fry Scholarship to the following dependents: a child or surviving spouse of a servicemember who dies on or after September 11, 2001, serving in a line of duty other than active duty, and a child or surviving spouse of a Selected Reserve member who dies on or after September 11, 2001, from a service-connected disability within four years after the date of the last discharge from active duty.