External tool needed: OBS Studio

Stream Settings in OBS Studio:
Custom Streaming Server
URL: rtmp://live-api.facebook.com:80/rtmp/
Stream key: get from this page: https://www.facebook.com/live/create
Uncheck Authentication

In OBS Studio, add Media Source the file
Click on Start Streaming (Controls, right portion)

In the https://www.facebook.com/live/create page, the video should appear