You can su to any user, if you know there password. (for sudo you need to be a sudoer, and know your own password).
So make the files readable and directory writeable(for deletion) by the other user, add files to a shared group, or use access-control-lists (ACLs) setfacl (What are the different ways to set file permissions, etc., on GNU/Linux?)
Then su other user Then do the move.
Also look at @roaima 's answer for how to do it without giving write access away to receiving user.