There are several ways on how you can download Facebook videos – some would ask you to install applications, but the safest ways are these two:
1) If you are using a computer, go to your Facebook page and place “www” with “m.” This will prompt you to the mobile Facebook site. Once there, click on the video you want to download and while the video is playing, right click on the video screen and select “Save video as”.
However, it is worthy to note that the quality of the video will change because you are definitely downloading it from a mobile site, and
2) If you don’t want to affect the video quality, all you have to do is download the Chrome Web Developer tools and then open Facebook on Chrome. Once there, open the video but do not play yet. Open the Chrome menu, select “Developer tools” and click the “Undock button”. Play the video from start to finish and then click the “Type” column and scroll down until you see the file labeled as “video/mp4”. Rich click on the video address and select “Open link in new tab”, and then select “Save video as.”
