How to make one mesh assume the shape of another?

The problem is this: I have an existing model that is rigged, UV-mapped and textured. The mesh was exported and edited in another package (the shape only) and reimported into Blender (no vertices were added or removed, although the order might’ve changed). The only information reimported with the mesh are the vertex positions, uv co-ords and faces, no vertex groups, weightings or anything else.

I now want the modified shape to be applied to the original mesh without losing the rigging and UV information. i.e. I want the changes to the shape, without losing the existing info.

In other words, I want to update the positions of all vertices in one mesh to that of vertices in another mesh.

Is it possible to do this?

In the Editing Context, in the Link ans Materials Panel, there is a menu labeled with the Me:. Change the mesh linked to your object by selecting that mesh from the dropdown.