Welcome to the Forum, looks as if your first post has a hint of trouble to come.
The bike you have by my reckoning started life as an A7 Longstroke, the engine of which which although sharing some parts with later engine types, the majority are not the same and care has to be taken selecting items that will fit.
The magneto is certainly not original, early type had auto advance, not manual, and the Lucas date code is from June 1954. The nameplate looks to be too new to be original, so all may not be as it seems. Look at that clutch lever bodge.
BSA Part number for a fixed magneto pinion is 67 540, retaining nut 24 195.
This link will help.
https://sites.google.com/site/priorymagnetos/spares-and-accessories To identify other parts, try this
https://draganfly.co.uk/product-category/bsa/sparesparts-for-bsa-a710-b3133-c101112-m202133/ Now head over to the introductions section and tell us all about how you got into this mess.
Swarfy.
