Transfering animations

Hey guys,

Is it possible to:

  1. Take a FBX file that contains a rigged, skinned character with animations.

  2. Somehow transfer the rigging, skinning and animations from the first character into my own character.

For example, could I take the rigged character and simply morph his mesh to get the shape of my character without messing up the skin weights and the armature bones?

What would be the best way to accomplish this task? Thank you.