When adding a Facebook Group to your Melon account, an additional step to include Melon as an 'App' is also required from your Facebook Group Settings page.  

1. From your Melon Studio, visit your Destinations page.

2. Click Add Destination and add your Facebook Profile first. Since your Profile is directly tied to your Group, add it to your Destinations even if you are not going to choose to live stream on your profile.

3. Now press Add Destination again and add your Facebook Group.

4. Click the modal to Open Group Settings or log into Facebook and visit your Group Settings and Apps page.

5. Type in "melon" in the provided search box and add Melon (Streaming) to your Group.

searh in group apps

6. Now test your connection by clicking Go Live, selecting your Facebook Group, and entering your stream title & description.

Also see...

Authorizing Facebook Group chat messages | Melon Support Center
Our guide to show your Facebook Group’s commenters’ avatars and usernames on your Melon Stream.