Guys, I am happy to report it is now done. I created a folder on the desktop machine, set it to share, then on the originating machine created a new network place at the location \\LAN IP address\folder name.
I have copied the files across. Or at least I think I have, I need to have a look around and see if there's any other stuff I've missed so far.
---------- Post added at 21:44 ---------- Previous post was at 21:39 ----------
To those of you who suggested using a flash disc, orf creating a CD ... of course, I could have - but I wouldn't have learned anything new, would I?