Problem solved now, and updated to 6.4.0 without any issues.
I've just updated the JFBConnect component @ Joomla 2.5 site.
Now the error shows the following:
PHP Fatal error: Class 'JOAuth2Client' not found in /components/com_jfbconnect/libraries/provider/google.php on line 48
How to fix this ? I can see in your forum, old post, that it has been an known issue.
We do currently not want to restore from backup, but possible if needed.