In addition, Unwrap UVW has a Save... and a Load... button. These let you write the UVs to a disk file and load in another Unwrap UVW, even in a different scene. But the topology will probably have to be the same (same vertex/faces count). If your new object is based on the original one and just vertices have been moved around, this method might help. Note that Unwrap UVW works on a single channel, so you might need multiple to transfer all channels.
It is of course also possible to write a quick script to copy the UVs, but it would have the same restictions regarding topology.
Bobo
VR Boboland
http://gfxcentral.com/bobo/