As long as export permits are in order, you shouldn't have a problem - someone like Irunguns, or Prophet River does this type of thing regularly. It would be more of an issue if it was on the restricted export list, but it isn't - to the US Gov, it's just an old 308 bolt gun.
BTW I am positively green with envy, and request - no, make that DEMAND a range report.
ETA - also the production date (Second World War) would make it C&R in the US.