UVMapper can export the UV information from an OBJ, and can apply that UV info to another OBJ. It can even grab just the UV info from an external OBJ and apply it to the loaded OBJ.
Of course, this only works if the OBJs have the same facet structure.

The UV information file saves with an .uvs extension. It may be useful to use UVMapper (the free Classic version would be just fine for this job) to extract the UVs from an OBJ file and inspect the resulting .uvs file.

If you distribute those new UVs as .uvs, you have the advantage of using a standard (sort of) format. It shouldn't be too difficult to write a Python script that parses an .uvs file and applies that information to an existing .obj file - or even, within Poser itself, to the loaded object, using TexVertices and TexPolygons

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