This is a question I recently searched for using Google. What I found is that there is no easy way on Facebook to download a video that has been posted by another party; however, I did find savefrom.net that will download a Facebook video providing you have the URL for the video.
To get the URL, simply right mouse click on the video, click on “show video URL”, then click on the “URL” (to highlight it), then hit “Ctrll+C” to copy the URL to the clipboard (or you can right mouse click and select “copy” which will copy the URL to the clipboard). After you have copied the URL to the clipboard, go to savefrom.net and enter the URL in the input field at the top of the main page. This action should present a download button where you can initiate the download (which will either be in MP4-HD or MP4-SD file formats).
With safefrom.net you can also download audio, video, and other types of files from various websites and social networks such as youtube.com, vk.com, vimeo.com, and others.
How to Download Facebook Videos Without Special Software (Ninja Trick!)
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