I have recently been able to deploy Firefox.exe  Patches with WSUS Package Publisher to clients. The normal 32bit and 64bit clients will be installed after deploying. During this period, It work perfectly in my company. This tutorial contains Step by Step deployment Guide with Screenshots. I hope this will help you to deploy Firefox to client.

Download offline Firefox.exe patches
1.https://www.mozilla.org/en-US/firefox/all/
2. https://ftp.mozilla.org/pub/firefox/releases/

You need to install Firefox.exe on testing PC. type C:\Program Files\Mozilla Firefox, right Firefox.exe, find the File version.
Wsus Package Publisher Deploy Firefox Step1

  1. Open the Wsus Package Publisher.
  2. Create an update for patches with Wsus Package Publisher .
  3. Choose Firefox EXE location.Wsus Package Publisher Deploy Firefox Step2
  4. Input the Detailed Information about Firefox.
    Wsus Package Publisher Deploy Firefox Step3
  5. As we publish a Firefox.exe file, an ‘Installed Rule’ is need to created by  ‘File Verison’ on Rule Type of drop down list. then click Add Rule.Wsus Package Publisher Deploy Firefox Step4
  6. Please input the detailed information below picture.Wsus Package Publisher Deploy Firefox Step5
  7. As we publish a Firefox.exe file, an ‘Installable Rule’ is need to created by  ‘File Verison’ on Rule Type of drop down list. then click Add Rule.Wsus Package Publisher Deploy Firefox Step6
  8. Please input the detailed information below picture.Wsus Package Publisher Deploy Firefox Step7
  9. Click ‘Next’ button again. then Click ‘Publish’ button.
  10. Wait a few minutes until you can see the update has been published.
  11. Right click the mouse on 3rd Party Software what you choose, Click the Approve button.
  12. Choose the Wsus Group what you want to apply Non Microsoft Patches (Third-Party Software), then Click ‘OK’ button.
  13. You can see the Firefox.exe is installed on client.

Source: http://www.sthshare.com/wordpress/how-to-deploy-firefox-exe-to-clients-silently-using-third-party-tools-wsus-package-publisher.html