I installed the Mozilla Build of Firefox by strictly following the installation guide at http://sourceforge.net/apps/mediawiki/ubuntuzilla/index.php?title=Main_Page#Installation
After succesfully finishing the installation, I CLOSED THE OLD VERSION of the browser, I went to the Applications menu, Internet and I launched "Mozilla Build of Firefox".
However, this still only launched the old 3.6 version of Firefox which was previously installed.
Then I rebooted the system, and then it worked.
Restarting the whole system just to get the newly installed mozilla build to work shoud definitely not be necessary. If it is unavoidable, then it should definitely be mentioned in the installation guide, as the last step: restart your computer.