Deny,
To do this, you would just need to add the IP address of the other server to the allowed hosts in MySQL. When you login to cPanel, go to the MySQL icon. At the bottom, there is a section to add hosts that will be allowed to connect to your databases. Enter the other server IP and then configure your script to connect.
If you need some additional help with this, open a ticket in the help desk and we'd be happy to give you a hand.