In order to move a domain please follow these steps:

1. Ensure you have a backup of the domain folder somewhere.

2. Download the domain folder using ftp and export and MySQL db's if used using PHPMyAdmin.

3. Remove the domain from the addon domains or parked domains section in cPanel

4. Login to the cPanel account for the destination domain and add the domain into addon domains or parked domains.

5. Upload the the contents of domain directory to the destination account using FTP 

6) Create MySQL db and user, and import the SQL file using PHPMyadmin

7) Edit the scripts config file and update the SQL user/ db name and password to those you created in step 6.