To migrate Plesk Billing from one server to another it is recommended to do a demo install on new server before hand, to make sure that the new server has a version of php and a configuration that can run Parallels Plesk Billing. Also:
1. Make sure your new server meets all requirements here:
2. Backup fileset and database and make sure that you add --default-character-set=utf8 to the mysql commands so that utf8 characters stay right. How to safely backup and restore a Plesk Billing MySQL database, please read:
2. Move the fileset and the database to new server.
3. Make sure you have the same domain name (the one used on the old server) set for web server configuration (on the new server).