** WARNING - THIS IS POSTED IN GOOD FAITH, BUT... changing your default web-browser may have consequences you have not thought of e.g. some users save their passwords in their web-browser
BACKUP YOUR SYSTEM AND PROCEED AT YOUR OWN RISK !**
If you, for whatever reason, have installed the web browser Firefox as a Flatpak from flathub, you will have found that you cannot make it your default web browser by pressing the button in the "settings" section. But there is a way that works on Ubuntu-Mate 20.04 (I have not yet tested it on 22.04).
You need to use the xdg-settings command. So open a terminal Ctrl+Alt+T, and continue as follows:
(1) To find out what is your current default browser type the command:
xdg-settings get default-web-browser
(2) To change it to your Flatpak version, the command would be:
xdg-settings set default-web-browser <your_flatpak_browser.desktop>
For Firefox this becomes:
xdg-settings set default-web-browser org.mozilla.firefox.desktop
source: [Setting a Flatpak app as the default web browser - Unix & Linux Stack Exchange]
(3) Close the terminal.
Please consider letting others know if this worked for you, or not, by posting on this thread. 