hi tonymuni, you'll find the download-links for offline installers for devediton at https://www.mozilla.org/en-US/firefox/developer/all/

This link simply downloads the stub and not the complete offline installer.

hmm, seems to work for all builds except the 32bit en-us one - not sure why that is... here would be the direct link for its full installer: https://download.mozilla.org/?product=firefox-aurora-latest&os=win&lang=en-US

The Aurora aka developers edition (and Nightly) channels are not really meant to be used like Releases with a Random build. They get checkins almost everyday so therefore they can get updates each of those days. This can sometimes cause issues until it is fixed, finished or reverted.

For example here are the May builds for Aurora and Nightly. https://ftp.mozilla.org/pub/firefox/nightly/2016/05/