I was trying out something that I don’t think it’s possible by default. That is Updating Windows using Mozilla Firefox browser.
When i browse to Windows Update using Firefox this is what I got.

So it’s not possible, but then you are able to update your Windows via WindizUpdate.
You’ll have to install the plugin from WindizUpdate and then you’ll be able to update your Windows using Firefox.
Take note that WindizUpdate is 3rd party plugin and is not affiliated with or authorized by Microsoft
** I’ve tested the plugin by updating Windows via Firefox and the plugin crashed! In my opinion, I think it’s better to update Windows via Internet Explorer but continue using Firefox to browse the internet.
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[...] Two days ago I talked about how to Update Windows using Mozilla Firefox. You’d have to install a third party unofficial plugin from another website which I do not recommend. [...]
A better way would be to use the IE Tab extension for Firefox, it allows you to choose between running the Gecko engine or IE core under Firefox tab in the case that a site doesn’t allow Firefox to run it.
That way, there is no need to even touch IE at all. It works fine in updating Windows for me.