That error is uncommon, but can happen with any extension when for some reason the installation is aborted when it's only partially complete. That means that the database is in an unknown state where some of the details about the extension are there, but others are missing.
My best suggestions are to:
* Uninstall JFBConnect
* Go to the Manage -> Database area of Joomla and click the "Fix" button to see if that corrects any inconsistencies
* Unzip and FTP the JFBConnect package to a directory on your server
* Use the "Install from directory" option, instead of uploading the zip file, which should help avoid any issues that arise
That's not a guarantee to fix things, but it's the first step to see if fixing things is easy. The next step would be to edit the #__extensions table and remove references to com_jfbconnect so that when it's re-installed, proper new rows will be added. I can give more details on that as necessary after you've tried the above.
I hope that helps,
Alex
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