I use to be able to livestream my meetings to my office facebook group. That option no longer comes up. It only gives me the option to go live to my page or go live to a "Share on your own timeline" or "Share to a page".
I also tried to go to Zoom chat and got nowhere with it. We use this feature weekly and are trying to figure out if it is gone for good or going to work again sometime.
Facebook changed their API for groups on April 23, making it so that you can no longer livestream to a group using the tools that you used to from zoom. The work around is use webinars and enable custom streaming service (custom RTMP), set up a live inside your group and connect the zoom setup. There is someone on the community forum that figured it out and I have used his method multiple times. It takes a few tries to get used to the steps, but it isn't bad once you do it a few times. His video can be seen here :https://vimeo.com/938818658/c3b7ebce44?share=copy
