Jane,
Yes, there is! Facebook uses it's own Open Graph tags to specify the title, image, and description for each page that is shared. Fortunately, JFBConnect fully supports the Open Graph protocol.
For a quick overview of the Open Graph capabilities of JFBConnect, see:
www.sourcecoast.com/jfbconnect/features/...pen-graph-for-joomla
What we'd recommend you do, is go into the Social configuration section of the JFBConnect administration area. Then, click the Open Graph tab. Make sure you enable Open Graph at the top, and then in the big box, set a default image to be used on all pages that are shared to facebook like:
image=http://site.com/link-to-logo.jpg
This will make sure that the information image is what's shared in all posts. Then, in any specific articles or pages, you can add the following tags to specify the best title, description and image per page:
{JFBCGraph title=Better title}
{JFBCGraph description=Better Description for this specific page}
{JFBCGraph image=http://site.com/better-image.jpg}
If you don't specify a title or description on the page, JFBConnect will use whatever the meta title and description for that page are automatically.. which is usually good enough.
Hope that all helps explain, and hope it's not too confusing. If you need anything else, just let us know!