That’s why you put up a maintenance mode panel with a message on old site after moving the data… then when folks get to the old site, they see the message and when they hit the new site, they just see the regular forum…
but there is no facility really to do what you want… you will have to manually copy over from the db any updates sftopics, sfposts, sfmessages, sfmembers, etc…. assume you are talking about posts here…
but even if you do that, if your new site has received new posts, you will receive conflicts because IDs would have been reused… and potentially topics will be out of order…
depending on number of posts, you could just manually enter the posts in the new forum as you… then use the forum tools and reassign the posts to the user who originally made them on the old site…