When you go live from a Page, you can download your videos from the Published tab of Creator Studio.
To download a single video:
Choose Videos or Live videos from the left-hand menu and find the video you want to download.
Hover over the video and click Download HD, or click the circle with the arrow pointing down and choose Download SD from the menu.
To download multiple videos:
Click the checkbox next to each video you want to download to select it.
Choose Download HD or Download SD from the options at the top of the table.
Note: If the video you want to download was an episode in a series, you'll need to click the circle with the arrow pointing down icon to see download options.
Your videos will download automatically. If the download doesn't start, refresh the page and try again.