Re: Transfer texture to another UV map

AFAIK there's no way to do exactly what you want, unless you are using one of the parametric mapping methods (e.g. cubic, spherical, etc.).

If the two objects are based on the same original -- meaning that you've just moved the points around -- you can actually use the posemorph tag to morph the UVs.

If the objects are completely different geometry you could try the Character>Managers>VAMP function to project the UVs from one object onto the other. It works pretty well if the objects have similar shapes, but otherwise ... not so much.