Bake texture to another object

Not sure if this is possible, but I got a one object A, that is nice textured. Another object had to be made, but it's a slightly different mesh, not that much though. (a few more edges, and vertices different bones, etc...) overall they look quite the same though. I cannot make the UV unwrap the same for object B.

And now, I wonder is it possible to bake the texture from A upon the modified object B, where B who would use the most nearby color of object A?