automatic FB group with update possible?

I bought something that when events are updated on FB then on my site also they are updated.

I like it very much... 

But it's exist also for groups?

I want to import groups in my site, when people post on FB, also updated in my site

When someone post on my site, it's also posted on FB with the busimatch logo as their avatar of FB. 

bump

 This question should be directed to the module creator that you bought the unknown module from.