In my humble opinion it has all the hall marks of European Beech just looking at the gain flow. It is from a plank of what we Brits call "through & through" plank sawn rather than quartered. Also an outsider could be Ash though I have only seen these stocks on low cost air rifles. The stock finish does leave a lot to be desired because the woods grain has been over contrasted with a dark stain, a gentler hand in the finishing and recoil pad fitting could improve matters no end.
I do feel that Birch is a non starter because Birch trees on this side of the pond do not put on large amounts of girth, also the timber has a large number of knots caused by the way the tree grows. To obtain a large enough plank size to be used for a stock blank would be just luck from an extremely old tree because Birch are what we here call Nurse trees, they are short lived and used to protect more valuable hardwoods Oak Ash and Beech in a newly planted plantation.