Can't figure something out in 3D Coat - can anyone help?

If I paint onto an object from a material (a 1024 x1024 jpg texture image I imported), the image is overlaid over the whole interface (as is the default). That's no problem and the painting works. I know how to hide that, but don't care.

But, if I use the alt key+mouse to reposition my object, so I can paint "behind" something which was obstructed before, only the object moves. Now the texture image is misaligned and I can't paint again in the original alignment.

Isn't there some way to lock the object and texture image together so a transform (move) affects both?

Or am I missing some better way to paint image textures onto objects.