If you enable the 'Social Profiles - EasySocial' plugin, you can configure which field data and avatars get imported in the JFBConnect backend > Profiles configuration area. Make sure to turn on the appropriate fields for the LinkedIn provider column and the "Always Import Profile Data" and "Import Avatar" settings are enabled. If you think you've set up this profile configuration correctly and the data is still not being imported correctly, please let us know and we can help you go from there.
-Melissa