hmm, well i dont have 6.5

but a quick solution i would take is:

-select the original dog

-shift select the uv'ed dog

-in animation menu: deform>create blendshape

and use the original dog as a blendshape on the uv'ed relaxed mesh. [after setting the blendshape value to 1 ofcourse] it should take the shape of the original no problems