Felix,

I doubt the gun fits your criteria for a WW1 production improved model D with the S prefix (indicating the patented double safety sear trigger).

This particular gun sounds like a much later , late model 'Standard' with the lengthened piston (with the patent number impressed into the piston skirt).

One way to find out would be if the stock had the letters 'BSA' in the checkering panels. The letters should be raised. If it does then it is not the gun you are after.

All the best

Lakey