I use phpbb I was wondering if I could use phpbb 's login on the rest of my website so that I just integrate the same login into my hole site and it would not let those that are banned post on the main site and it would be able to know if it was a moderator a user or admin so that those could be types of accounts.

and so the whole site could be moderated by the same moderators/Admin

Well what you would use is to retrieve the data from the cookie that phpBB puts on the user's computer. Also, you could look into the MySQL database and write a script to retrieve the data from that table.

I know that Jokeroo.com uses this kind of environment.