The trick is actually to create a folder inside the email group. Put all your emails inside that folder. Then move the folder to the new email group.
We aren't on E9 anymore but this worked for us before. We've reported the bug to Eloqua months ago but I don't think anything was done. All your emails will still be linked to the original email group but again if this is just for archival/organizational purposes then it does "trick" Eloqua into moving it. This is surely a bug so I hold no responsibility for this if it still works.