How do I save a live video on Instagram to my phone's camera roll?
After you've ended a live broadcast on Instagram, you can tap Download Video to save the video to your phone's camera roll. Keep in mind that only the video is saved, and not things like comments, likes and viewers.
You're only able to save a live broadcast right after you've ended it. Only you will see the option to save your live video.
Note: It may take a minute for a live broadcast to save to your phone, especially for longer videos.