Save the original image with the layer group as an xcf. In the new image, and open the original as layers (
File > Open as Layers). This will add all of the layers from the original image.You'll need to delete the layers from the new image that you don't want. Unfortunately you can't pick/choose what layers you import. But as long as this is only a one-time transfer (i.e. you don't need to copy/paste the layer group back and forth) this should work.