"S" 1St Variation No4MkI Cocking Piece

I have a 1942 No4 MkI Marked B 1942,K6273 on the left side of the receiver socket. B is on the safety lever, B on the fore stock near the brazed trigger guard. "England"above a "Crown GP"on the right of the receiver ring and the "NP .303"2.22 18/2 TONS" on the right side of the barrel near the muzzle. The bolt has a small "Square S"on the bolt handle near the bolt body. The bolt handle also has a small "Crown GP". The 1st Variation cocking piece has a small "Square S". FR is stamped on the right side of the butt stock. From my research this rifle appears to be a BSA , English Export, Indian rebuild? Did Savage make the 1st Variation cocking pieces? I would appreciate your input. Thank you!

Savage did make a 1st variation cocking piece