What is the Content - Community Builder Author plugin? That's not from JFBConnect. Is that an EasyBlog plugin, or from a 3rd party vendor? You may need to contact that developer to understand what they are doing that's causing a conflict. When the login doesn't complete, what actually happens? Do you get an error message, a white page, 'nothing', etc?
If you need more help from us, we may need to know the site URL to see what errors are happening. Can you please post (or Private Message) just the URL? We don't need credentials yet. To PM me, hit the arrow under my name (<----) and hit the mail icon.
Thanks,
Alex