This was the only thing that worked for me after upgrading to Ubuntu 22.10.
First, remove the Snap version of Firefox:
sudo snap remove firefox
(If you have settings in the Snap version of Firefox under ~/snap/firefox/, you may want to migrate those to ~/.mozilla/firefox/)
Then add the PPA from mozillateam:
sudo add-apt-repository ppa:mozillateam/ppa
Now, the package firefox is provided by both the Ubuntu repos and the Mozilla PPA. The version provided in the Ubuntu repos is a transitional package that actually installs the Snap version of Firefox behind the scenes, which in this case, we don't want. Check that you can see both firefox packages by running:
apt info -a firefox
To prevent the installation of the Snap version of Firefox through the firefox package provided by Ubuntu, we need to modify this file as root, using gnome-text-editor or whichever text editor you prefer:
sudo gnome-text-editor /etc/apt/preferences.d/mozillafirefoxppa
Add these lines:
Package: firefox*
Pin: release o=LP-PPA-mozillateam
Pin-Priority: 501
Package: firefox*
Pin: release o=Ubuntu
Pin-Priority: -1
The first three lines give priority to the firefox packages provided by the Mozilla PPA. And the last three lines disable installing the firefox packages from Ubuntu's repositories.
Run sudo apt update to make sure the changes have been taken into account.
Now, you should be able to install the PPA version of Firefox. You can simulate an installation of Firefox using --dry-run, like this, so as to check which version of Firefox will be installed:
sudo apt install --verbose-versions --dry-run firefox
If you don't see the word snap in the version number of the firefox package (for example: 1:1snap1-0ubuntu2), you are good to go. Run this command to install Firefox (without Snap):
sudo apt install --verbose-versions firefox