FBTake's answer:
Repost Video for FB - Repost Video for FB is a social app that comes up with features to help you in downloading your favorite Facebook video to your mobile phone in the desired format so you can watch it irrespective of being online or offline.
FDOWN.net - Download Facebook videos and save them without using Java or installing software.
Video Downloader for Facebook - Video Downloader for Facebook is the best-in-class FB video downloader for browsing and downloading the favorite video with a single tap.
SnapSave - SnapSave allows you to download your favorite Facebook Videos in HD qualities, including 1080p, 2K, and 4k on any device.
Repost & Story Downloader - Repost & Story Downloader app offers features that let you check your Instagram followers so you can keep track of your social life.
FastVid - FastVid offers a Video Downloader for Facebook that allows you to select any video from FB, copy its URL, paste it into the field, and click on download to save it to your device.