Animation for FPS game with two skeletal meshes

I’m creating an FPS game, and set up two skeletal meshes, one for first-person view (only arms and hands),
one for other players to see (a full body). The gun is attached to the right hand in first person view.

When I look at the player from another players perspective, the gun is there, but it’s not animating with the full body.
How would you solve this problem, and make the gun animate with both meshes?