A screensaver is a file with .scr extension. Just copy it to a pen drive and copy it to the same location on the desktop.

But a copy of an exe sometimes becomes a shortcut (although it shouldn't do that if you copy across devices). Then you press control so you see a little plus sign.
And set the view in Explorer to detail and the folder options to "not hide extensions of known file types". Then you can easily monitor both the full filename (it shouldn't become a .lnk) and the filesize (it should stay the same).

If both the full filename and the filesize and the location on both machines are the same it should run, unless - of course - it needs other files (like a picture showing screensaver needs it's pictures) or depends on registry settings. If so, please post the full and exact error message you get (which surely isn't "shortcut argh"), when you get it, and the name of the screensaver.