If your WordPress website is hosted on cPanel currently with another hosting provider, then you are able to migrate the entire cPanel account using our Migration Center...
https://support.brixly.uk/knowledgebase/article/how-to-migrate-your-cpanel-account-via-the-migration-center
However, if your WordPress installation is not hosted on cPanel, you are still able to migrate this using the Softaculous tool.
Brixly provides Softaculous as a one-click application installer, which provides you with the ability to import a remote WordPress installation. This makes migrating WordPress sites a breeze!
Migrate a WordPress installation with Softaculous -
https://support.brixly.uk/knowledgebase/article/migrate-a-wordpress-site-from-a-remote-server-using-softaculous-remote-import
Once you've migrated your site you'll want to test it before making changes to your DNS...
https://support.brixly.uk/knowledgebase/article/brixly-cpanel-website-preview
Finally you'll want to update your DNS - either by switching the name servers for your domain to Brixly's or by adding appropriate A records to point at your Brixly servers IP address.