Private Facebook Group Integration

We have an online program that has a private Facebook group. It would be really helpful to have some sort of integration between the two. Currently, I include the link to the group in the member section and then when we receive invite requests, I have to cross reference it to our membership list to see if they are signed up for our program. I looked at the Ultimate Facebook plugin, but do not see this type of feature included. If there was a way to better integrate with Facebook Groups, that would save a lot of manual checking on our end. Thanks for the consideration!