Need help identifying a Luger S/42

[shogun17]

Hello Everyone,
I finally picked up a Luger (old childhood dream) but I need your knowledgeable help to identify the what it really is:
SN # 4422 gothic letter b under the frame
SN# 3283 gothic letter a under the barrel
Inside the wood grips it is stamped 22
on the toggle it says S/42 and then 24
on the side is says 95 with a Crowned gothic B and has 2 Mcrown and a smaller eagle
on the barrel there is a smaller eagle again
I can see a blued barrel base
Black bekelite magazine
A 9mm cartrige fits in the magazine and the chamber but I don't know what is the caliber actually need help with that too.

Any idea on the caliber, year ?
Many thanks
dan