Short answer, this should be automatically taken care of if you are using at least JFBConnect version 6.4.
Alex wrote a
blog post
awhile ago for API v2.0 deprecated. In it he laid out a quick timeline of the API deprecations and the corresponding versions of JFBConnect that you should be using. The section for this timeline is titled "What do I need to do?"
I just did a quick glance on the
Facebook upgrade guide
to refresh myself on changes from 2.1 to 2.2 and it's all related to Page and Group access. We'd already converted our Channels features to use the page access tokens quite awhile ago and many users have been using newer versions of the API/JFBConnect which require this with no issues.
-Melissa