This was possible two years ago when we tried it...not sure if anything has changed, but it should still work. There are several files to copy and put in the exact same locations.

There's a game client folder in program files, usually called zenimax online. Move and create an exact replica.

There's sometimes an Elder Scrolls folder in my documents...same deal, exact copy. Although this is character data...they'll rebuild themselves if you don't move them.

There's a launcher in zenimax online...launcher...Bethesda.net. Once files are copied, this should launch the app and run the same as the other system. You might get a one-time pop up about using a new IP.

Things I remember being problematic: lots of posts about Steam issues (shocker), so the process might be more complex if you're using Steam. I also remember posts warning not to try to move servers via this process.