If you run Mozilla Firefox as a regular user on Ubuntu or any other flavour of Linux, it will not update itsself automatically, because it lacks the neccessary system rights to do so.
To update Mozilla Fireofx on Ubuntu Linux just start Firefox with root rights like so:
sudo firefox
You can then click the Update Firefox menu option in the Help menu and Firefox will update itsself immediately. Only, if a new version is availlable, of course.
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