Hi Roger, yes birch is a definite possibility but as the stock is quite dark it is difficult to say for sure one way or the other.
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A factory new 1942 Long Branch would have walnut or birch furniture and an alloy buttplate.
Thank you all, I will order a NOS birtch stock with an alloy butt plate.
For your benefit, I have 3D modeled my current buttstock and have a Haas mill cutting chips in magnesium for a replacement butt stock. In a moment it will leave to be powder coated pink. The lava lamp insert will come back about the time the stock comes back from coating, but the snow globe insert will take a little longer as will the reservoir marked "Bindi's tears." In a few weeks hence the adjustable cheekpiece made of mammoth ivory will come in as will the adjustable butt plate with neon insert reading "Whatever pleases the current owner is correct." I will offer my replacement butt stock for sale for a small fee.
I would go with walnut. Long Branch rifles seem to be mostly walnut
All theLB wood I have bought over the last 30 odd years is mostly walnut by a long shot
Which raises another important issue; the OP did in fact ask what wood the rifle would have left Long Branch wearing in 1942, so the answers given are pertinent. However, as it was indeed FTR'ed at Faz it will probably have been converted to Mk1/3 spec., & have a hung trigger, as Lee Enfield intimates. This means that it will need a forend of Mk2 type (with the cross bolt at the back end rather than the tie plate). Another reason to 'work around the existing forend' if at all possible, in doing any rewooding. If the current forend is now a good fit & not too bad cosmetically it is probably best left as is. The replacement of the butt & guards is far less critical. A photo of the woodwork on the rifle in question might be helpful here.