Here's another option: a stand-alone Windows utility which is fairly ancient and should work on any machine.

http://www.uv2uv.spacymen.com/

It does exactly what you want, assuming I've understood you properly. The inputs are two OBJ files composed only of triangles, with your source and destination UV mappings; and a texture map for the source OBJ which has to be in BMP format. The output is the map transformed to fit the destination OBJ, also in BMP format.

Converting back and forth is an extra few steps, but easy enough to do. UVMapper will triangulate the input meshes for you; you don't have to keep those interim files of course.