In case one needs to download a video from Facebook there are some considerations (besides from ownership and copyright).

First of all, videos found on Facebook are very often shared from another online source, e.g. YouTube. In order to access the video in the best quality - and as a bonus get background information such as "who, when, and why" - it is recommended to do a search for the original source: Use meaningful search phrases such as video title (if given), topic, named entities (e.g. places, people). Do this in your browser using your preferred search engine, and switch to the "videos" category in the search. Often, one can find a promising result from thumbnails, playing time, and title.

If the original video is found, it can be downloaded using Video Download-Helper, or Jdownloader2, unless the owner of the original video has specifically protected it.

If the video cannot be found elsewhere, or if you simply prefer to download it directly without looking for original sources there are several solutions. It should be noted that they will only work for videos that have been made publically accessible. Private posts shared and spread widely are still private, connected to the original private account where the source was posted, and in such cases download attempts will be blocked.

If a video is public and can be downloaded, it is possible to edit the video URL in order to get the mobile version which is downloadable, but not in the highest quality (as described in the video tutorial).

The fastest solution for getting the video in a better quality without any applications installed will be from using a third party service, such as fdown.net (recommended in the video tutorial from PCMag).

Paste the Facebook video URL from the share option (see video tutorial if needed), and use the download button to save the video file locally.

Online service for direct downloads:
fdown.net