This is a customized BSA Martini Cadet rifle built on a Martini falling block action. BSA made these rifles for use by the Australian military cadets starting in the late 1890’s.
After WWII, many were converted to sporting or target rifles by gunmakers like Sportco, and the original Cadets as well as their Sportco conversions were imported into the United States starting in the late 1950’s, so absent of any markings it is impossible to tell who customized the rifle or when.
The rifle has a pistol grip, Rosewood grip cap, Monte Carlo comb, cheekpiece, and an ebony nosecap on the beavertail forend.