If you are worried that something might go wrong then all you have to do is have the board installed in site A and see if anything goes wrong. If all is OK and I gather it must since you probably have one board right now then take the whole folder of ubbthreads and put it on server domain B. Then change the config.inc.php information to connect with the second username and password (bare in mind that you need to create one of those and give it access in your live database).
Then you will have to manipulate your stylesheets to grab the right images for each board but you will need to keep the same names for those stylesheets. So for instance if you are using the ultradevblue on site A with the header1.png file you need to keep the same name for the stylesheet for the second board and a) either replace the header1.png file with another image (same name) or b) change the stylesheet of board B to use the header2.png.
Frames are not recommended.
If you want to see a live example then go to
www.ultimatenurse.com and
www.nurseserver.com. Both sites use the same database, they have a different license of ubbthreads and use different stylesheets and images.
