Open the Facebook Live video you want to save
Click the three-dot menu on the video
Select Download video if the option is available
If Download video is not available, copy the video link
Use a trusted third-party Facebook video downloader
Paste the copied link into the downloader
Choose the video quality you want
Click the download button
Save the file to your device
If the live video is your own, check the Video Library or Creator Studio for download options
If the video is private or restricted, downloading may not be possible