Currently there is no possibility to easily download Facebook videos (from the browser site I mean, not from the app Facebook),
as does Google Chrome instead.
It used to be possible, but now it's only possible with images:
hold down and the menu with the possibility of downloading the image exits.
For videos, however, no, while in Google Chrome it is simple and the same procedure is performed as for photos.
I specify that it does not depend on the type of video or its privacy.
Chrome allows you to download any video, while Opera (mobile) unfortunately doesn't.