I noticed that new forum is not using IPB and all accounts are now unusable for mew forum. They work only at old.bestblackforum.com .
—- 1. Using facebook / twitter login will be easy but most of user avoid social login in forums.
You can use old Facebook app for new forum so users will not have to approve login as they already have apporved Facebook Login at old forum.
- Import old accounts to new forum.
You can do it by 3 ways and its big benifit for all us. Creating new account is annoying.
Way 1. Export old database on your system and modify accordingly to new forum database . And then import users accounts ( null some tables) like profile photo . bg_photo status.
Way 2. Create custom login with OLD BFF . It will work in same way as facebook login works but you users have to approve login from http://old.bestblackforum.com ( they have good api documentation)
Way 3. Use CUSTOM LOGIN - IPB has a option and if you are SITECORE on new forum they have modules as well and apis.