On Facebook, the option to “Download Images” was introduced a few years ago. You can basically do this by just going to the image and clicking on “Options” in the bottom right corner or on the three dots on the top right in the app.
Just like Instagram and taking screenshots of posts there, there’s this misconception that if you download an image that someone has uploaded they might get a notification from it. You can rest assured that the user will not be notified if you download an image they’ve uploaded.
As long as the image is public or available with the privacy settings the person has then you can download it without the person being notified about it!