Can u not update Firefox from the Application Menu>Help>about dialog ?
Apparently not I see …
I use Firefox Developer and you can update there from said dialog.
Download via Firefox Developer Edition
Last used https://download.mozilla.org/?product=firefox-devedition-latest-ssl&os=linux64&lang=en-GB
mkdir -p /opt/mozilla/firefox/developer
tar --overwrite -xpf <path>/firefox-dev.tar.bz2 -C /opt/mozilla/firefox/developer # creates sub dir firefox
ln -s /opt/mozilla/firefox/developer/firefox/firefox-bin /usr/bin/firefox-dev
\cp -f <path>/firefox-dev.desktop /usr/share/applications/firefox-dev.desktop
Can’t recall where the .desktop file came from but contents are ;
[Desktop Entry]
Name=Firefox Developer Edition
GenericName=Web Browser
Exec=/usr/bin/firefox-dev %u
Icon=/opt/mozilla/firefox/developer/firefox/browser/chrome/icons/default/default128.png
Terminal=false
Type=Application
MimeType=text/html;text/xml;application/xhtml+xml;application/vnd.mozilla.xul+xml;text/mml;x-scheme-handler/http;x-scheme-handler/https;
StartupNotify=true
Categories=Network;WebBrowser;
Keywords=web;browser;internet;
Actions=new-window;new-private-window;
StartupWMClass=Firefox Developer Edition
[Desktop Action new-window]
Name=Open a New Window
Exec=/usr/bin/firefox-dev %u
[Desktop Action new-private-window]
Name=Open a New Private Window
Exec=/usr/bin/firefox-dev --private-window %u
(Maybe the downloaded (as opposed OS pre-installed) version of FF standard allows you to update too, dunno, haven’t tried it)