I tried RSS Graffiti on a Facebook Group and it worked too! (I had an error in the beginning, but after a while it worked out... mystery.)
- On FB search box, type "RSS Graffiti", and click on the link
- Once you're on RSS Graffiti, click on "Add to my Page", underneath the profile logo
- Select the page you want to add
- Now, go to your FB page and select "Edit page" underneath the profile picture
- Scroll down, find "RSS Graffiti" and hit "Edit"
- Click the green button "Add a feed"
- Then paste your Twitter URL. (How to get your Twitter URL? Go to your Twitter account. Under profile, you'll see a RSS icon on the right pane. Click on it, and copy the URL).
- Click on generate and preview.
- Customize and save your style, such as click on "strip twitter username" and select the style as compact, to allow "comment/like/share"