SHt LE BSA Butt-stock Markings

[nijalninja]

G'day there, just have my old BSA that I've been wanting to trace the history on a little. I got pictures of ABSOLUTELY EVERY marking on every inch of this Rifle, and took notes too, but first I want to start with the Butt-Stock since the markings are pretty obvious.
Attachment 89115
I have no idea what anything apart from the 'III*' part means, but the '83370' is also stamped on the action near the barrel. Knowing that the barrel and action match, and that this number is the same, could I assume the butt-stock is matching as well?
Attachment 89116
Any info is greatly appreciated.

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