Since Firefox can only send one user agent string per request, it's hard to think of a way to make your carrier believe you're on Android but make the site believe you're on Windows or MacOS.

If you are using a secure connection, what is sent inside the encrypted tunnel is invisible to your carrier, so for that kind of connection you could try using an extension that lets you assign specific user agent strings to specific sites. One I've used (it doesn't have the best interface, though...) is: https://addons.mozilla.org/firefox/addon/ua-site-switch/

If that's no use, maybe there's a trick someone has learned that you could discover in an Android forum? I generally consult this one: http://forums.androidcentral.com/

Or of course you probably could pay your carrier more to solve this problem and not worry about potential contractual penalties or cancellation.

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