It's not beech, grain is too tight an linear.
Longbranch intermittently used maple on rifles from 43 through 44, and this looks to be one of those. They are usually stained a deep mahogany color, and this one has lost its color, either in service or it's been lightly sanded at some point. For watever reasons, a lot of the LB maple stocked rifles went to new zealand - the two I owned were NZ stamped - not sure if this one is or not.
In late 44 and 45, you also sometiems see LB rifles with left over Savage wood - but that stock is clearly not birch.