Yes, you can. You will need to upgrade your UBB.classic board to 6.7.2 (the current version) first, though. It has an import/export feature that will export your data (users, categories, forums, and posts) to files. After setting up your UBB.threads board, you will then use the files that you created to import the content into your UBB.threads board.
You can find the details on in the UBB.threads
Admin Guide. If you do not have a current subscription to the Members Area for your UBB.classic license (to download version 6.7.2), we can provide the files to you.