If you are running a fairly current version (>5.0.80) and it appears from our records that you are, you should be able to install the admin portion onto the new machine and simply copy the licenses folder from the old machine to the new machine (also, make a backup of the licenses folder, preferably on a floppy or some other removable media).
Then run licenseadmin on the new machine to see if the license(s) and users show up. If they do, all is fine and you should delete the admin portion from the old licenseadmin server. (just dump the ICETCP5 Server folder in Program Files->Jriver into the recycle bin).
If the users DON'T show up on the new server, enter the company name and License keys from the old server, exit the licenseadmin program, copy the licenses folder over from the old server again and rerun licenaseadmin. You should see the licenses now.
Note that this means the links to configwizard on the individual PC's will now be wrong but that isn't a problem because you won't need to run configwizard again unless you do a reinstall of the client portion. If you need to do a client reinstall or new client install, simply BROWSE to the new TCP5_USER share that you created on the NEW licenseadmin server (which you should have shared with permissions of full control for all) and run the setup in there. The resulting install will have the correct link to config wizard.