Many Facebook download problems are really file-location problems. The browser saves the file, but the user expects it to appear in a different app.
iPhone and iPad
Safari usually saves into the Files app under Downloads. Open Files first, then move the video or image into Photos if you want it there.
If you downloaded from an in-app browser, repeat the save in Safari for a clearer download prompt.
Android
Chrome and most Android browsers save into Downloads. Open Files, My Files, or Downloads if Gallery does not show the item immediately.
If the browser asks for permission, allow file downloads and try again.
Three tools with browser downloads
These options run in the browser, so the final file location is controlled by your device and browser settings.
Use your browser download list if you are not sure where the file landed.
Windows and Mac
Desktop browsers usually save into Downloads unless you changed the default folder.
Chrome, Edge, Firefox, and Safari all have a downloads list. Open it to reveal the file location instead of searching manually.