I received the following response from my service provider:

-----beginning of email-----

Hello,

We can allow you to move to one of the newer servers running the following

mysql Distrib 4.1.18,
PHP 4.3.10 (cgi)

Relocating to the new server involves the following steps:

1. We create the account on the server that matches your requested plan type
2. After receiving the login info - you need to upload the site to the new server and configure it to your liking (users, e-mails, cgi scripts, etc.)
3. After testing the site - you request a DNS change to point your domain(s) to the new IP address.
4. The DNS change takes 6-8 hours and after a safe period of time (1-2 days) we proceed with deletion of your old site.

Please make sure that you understand the steps involved and advise us of your decision.

-----end of email-----

I transferred UBB Classic (cgi files) from one server to another, however, I never transferred UBB Threads (php files) from one server to another, therefore, in preparation for version 7, with transferring these php and other files, how do I also transfer the database itself, or do I need to concern myself about transferring the database?