I am evaluating MyBB and some other forum software packages for a client. I have a question regarding the archiving of old threads/posts/categories. Is this possible with this forum software? If not, is there a module that can extend MyBB with this capability? Any information would be greatly appreciated.
You can prune them but that deletes them. But you can manually or automatically move threads to a forum that is visible to just admins, staff team, or everyone.
Take a look at Configuration -> Custom Moderator Tools.
In short, create new archive forum(s), make it/them closed in options, then create a tool which moves the topic to that/those archive forum(s). After that mods/admins will be able to use that tool in the same place as other tools (close/open, delete, move).