The good thing is that it’s not that difficult, if you understand MySQL, PHP and obviously are aware of where the actual files and folders are located for the original install. If you do NOT know this information, I would hire someone.
Obviously, you should make a good backup of the site and database. The next thing is to use PHPMyAdmin (I use WHM/cPanel, you have to apply these instructions to whatever you use accordingly) to make a backup of the original database. You should also download all the files and folders of the original install. On your new domain, use cPanel or whatever you use, to create a new database with the same user and password of the old to make it a bit easier. You can find this information in your original configuration.php file. Then import, to the new database on the new domain, the export of the original database from the original domain. Got it?
Look at your configuration file and make sure everything is updated to reflect the new location and that all directories are in place especially if you followed their instructions to secure WHMCS. Make sure the database name, database user name and password are accurate. Upload all the necessary files to the new domain. Visit your WHMCS admin area, it will kick you a license error if you didn’t already visit their website and reissue the license. Once you do that, you should be able to login with the same credentials you used before. Visit “Setup > General Settings” and update your domain listed in those boxes. Everything should be ready to go. My relocation was absolutely painless.
Don’t forget to delete you old install after you are sure that everything is cool with your new WHMCS install. There is no need having that in the wild not getting updated on your old domain.