Two basic ways that really work.
How to download videos from Facebook to your computer or Android device
This can be done without the help of third-party programs. Copy the link to the desired video on Facebook and paste it into any of the following web services designed to download video from the Web. Then select the quality of the final file and click on the download button. After a while, the video will appear on your device.
Popular web services that let you download videos from Facebook include Video Grabber, TubeOffline, 9xbuddy, KeepVid, SaveFrom, YooDownload, VideoGrabby and Catchvideo.net.
How to download videos from Facebook to your iPhone or iPad
This method is almost identical to the previous one: you can download videos to iOS using the same web services. Only in addition, you will have to install a special program. The fact is that Safari, the standard browser in iOS, doesn’t allow you to download videos from the web. So you will need a free DManager application, which is a hybrid of browser and file manager.
Next, use DManager to open the site of any service mentioned in the previous paragraph of this article. Then paste the link to the video in the text box that appears, select the destination file options and click on the download button.
Once the file has been downloaded, click on its name. When the media player starts, click on the three dots below the video and select “Send” → “Save Video”. The video will appear in the device gallery.