Can I connect FB Groups, Comments, and a Website for cross communication?

I’m looking for a plugin that allows me to connect a website to Facebook to allow for cross communication, especially with FB Groups.

For example, I want a web page to be able to display all or latest activity from a FB Group and vice-versa. A website member can comment on any of the FB Group post on the web page and have their comment show up in the FB Group under the post they commented on. If someone reply to the website member’s comment inside the FB Group, it will show up on the web page. So there is truly a cross communication between the website and FB groups.

And there is options to enable anonymity when activity is grabbed from the FB page and displayed on the web page. But there wouldn’t be a need for anonymity most of the time because everyone on the website will need to be identified and verified through Facebook.

Is there anything remotely similar? If not, I’m going ahead to develop it. If anyone have advice or can point me in the right direction to help me as I develop this plugin, please do.

I can code this myself. If there is any resource out there that can help, let me know. Thank you.