Dagofee,
I'm not sure I'm understanding exactly what you're trying to do, so I have a few suggestions which may hopefully help.
Alright, so your goal is to let user's invite their friends from Facebook. I'm not sure why they need to log out though. One thing you can do is have them re-connect or map their Facebook accounts to their JomSocial/Joomla account. This can be done by just having them click the Login With Facebook button if they're already logged into your Joomla site. No need to logout first.
There's 2 caveats to this:
1) You'll have to add the { JFBCLogin} text to the template file of the Invite module. Just add it above where you're telling the user to logout, instead.
2) You'll want to make the changes to the JFBCLogin tag to make sure it appears even when a user is logged into Joomla. Just read from the post I link to on down, the rest is regarding a different issue:
www.sourcecoast.com/forums/topic?id=1618&p=2#p7399
With that, there's 2 bonuses: It should get more users to sync there accounts, and is less confusing. We're planning on implementing both of these changes in upcoming releases of the Invite module and component (for the JFBCLogin tag)
Finally, one thing I'm unsure about is before you moved to JFBConnect if you had a lot of users that were using the JomSocial Facebook Connect functionality. If so, and you need to migrate those connections over, make sure you read the section about importing from 3rd party connections in the config guide below:
www.sourcecoast.com/extensions/jfbconnec...ration-guide?start=9
Hope this all helps, and sorry to make you go around modifying our stuff! If you have any questions, let us know.. and thanks for letting us know how you're using the component. Always good to hear example usage cases as it helps us make things better in the future!