Moving animated bodypart with the body?

Hi everyone!
Currently I'm working on a 2D game, in which I have an animated character and his right arm is separated from his body.
The running animation's length is 30 frames, and the separate "running arm" animation's length is also 30 frames, so I'm making it a child of the character's gameobject, and everything works fine.
But I have a "shooting arm" animation, which is 10 frames long. I can change between the "running arm" and "shooting arm" animations, but the problem is: I can't make the arm follow the movement of his shoulder. How can I achieve that?
I'm attaching a short video, so you can see it in action: