In contrast to all other MSI-files discussed here, there are no such files available for Firefox from Mozilla. Mozilla offers only an installer of kind setup.exe. That installer does not internally base on MSI, so it is not possible to extract an MSI-file from it.
Here are some of your options:
Copy the program directory to a server and let the clients run it from there
This works, but has some disadvantages:
wait until Mozilla offers MSI-files
There are discussions inside Mozilla to provide MSI files (e.g. in bug reports 598647 and 231062), but the files are not yet available for download, and it's unclear how long that will take. The discussions are ongoing since many years.
use MSI-files from Frontmotion
They offer some free service, and also payed support contracts, that can include individual configuration changes according to your specific needs.
I'm reluctant to use such offers because
use the package from Bespoke I/O
Used to be similar offer like Frontmotion, now free but no support any more.
somehow script the installer.exe
install with command-line option -ms, use helper.exe for uninstall.
Use the "setup.exe wrapped in MSI" trick using custom-actions of windows-installer.
It seems that the program "Windows Installer Wrapper Wizard" isn't available any more. Alternatively XML-files for WiX are available that also use the wrapper trick, but some of them even don't include an uninstall feature.
Use imaging tools like WinInstall LE.
Disadvantage: MSI-files created with such tools are unreliable.
Use "Exe-To-MSI" converter
This records and later plays back the keystrokes that are needed to install the setup.exe
Interesting idea, haven't tried this one yet.
create firefox.msi yourself with AdvancedInstaller
My walkthrough shows step by step how to do this, using only the free features of AdvancedInstaller.
create firefox.msi yourself with WiX
Slightly more difficult to set up than AdvancedInstaller, but then creating the file every six weeks is less work. And it's more automatic, so there are fewer chances to make a mistake.