Hello! At the moment, to import images from a skin, you'll need to drag each attachment/mesh from one skeleton to the other while the same skin is active in both skeletons, change skin and repeat the process.
It may be easier to remove skins from the source skeleton, import the images at once, then populate the receiving skeleton with the meshes in the correct skin placeholders.
Another option which is theoretically possible but I'd have to test it to be sure is to export a json from the source skeleton, and import it in the receiving skeleton. Since it works for jsons exported from photoshop, there's a chance it may also manage to import the skins in your project. We have never tried to use it this way though, so I can't guarantee it will work as expected.
Moving elements across skeletons is a relatively new feature so it can be perfected further. We'll take your feedback into consideration, thank you!