bbPress Export and Import Plugin is a plugin you can use to export and import bbPress topic, replies and forums. Before using it you should import your users to your new site, there some plugins you can use from bbPress but I use this one: https://wordpress.org/plugins/import-users-from-csv-with-meta/ now after doing that than you go in panel of your old website and go to the forum category you want to export and click on the export link:
Than you go to the new website go to the forum where you want to import the topic and replies and click on the browse button and then click the Run import
Notes: you need to have a real good server configuration to do this or you will get gateways timeouts.
I did this in this forums and bruh is was not easy 🙂