Maya Animation :: Reconnect Soft Modifications On Identical Mesh?

I'm working on a animation with a female model. It's a simple animation which I did with a couple of soft modification points. After that was done, I created the UV texture in Photoshop. At the point in the animation that the soft modification points deform the mesh the texture goes all crazy.

I know why that is, because the UV is projected and is not stuck on the mesh yet. I've worked the wrong way. Next time I will first add the UV texture and then animate the mesh. Now I'm having a duplicate of the model and deleted the history. The UV sticks on that mesh, but the softmodification points are also deleted. So the mesh doesn't deform anymore.

I've tried a lot of ways, but didn't find the solution yet. That's why my question is. How do you copy/reconnect the soft modification points on a identical mesh with a sticking UV texture? It's the same polycount, so I think it's possible. I've tried connecting the soft mods in the new mesh in the Hypergraph, but I didn't know which atributes I should connect. I also tried to bake a simulation, but Maya says he is calculating, but I can't see if it is working and how long it would take. I tried to export the animation and import it in a new scene with the history deleted model, but that wasn't the solution either.

I don't know if my story is all clear, but this i my goal. I want the animation on a model that has the UV texture sticking on it. What is the best way to get there?