On two humanoids, animation works in different ways.

The skeleton is assigned the same. The same number of bones at the hands.

As you can see in the video, when moving, the character's left hand moves up and down. The original humanoid behaves in a different way - his hands do not move. How can I fix this? Which way should I move to fix this problem?

 

I would use IK to keep the hand on the barrel of the gun.