Android...
Open the Facebook video you want to download in the Facebook app or the website
On the app, hit share and then tap Copy Link. On the website, copy the link in the URL bar
Open fbdown.net in a browser that supports downloading. Most Android browsers do, including Chrome
Paste the link where it asks you to and click Download
On the next page, tap and hold on the quality — normal or HD — you desire if you're using Chrome. On Firefox, just tap on the link, and then tap and hold on the video
Choose Download Link in Chrome, Save Video