I don't think there's many situations where you'd have to abbreviate Firefox anyway, it's not a large word to begin with. Internet Explorer as IE I can understand, it's large and compounding it is useful - but we don't abbreviate Opera or Chrome?
All the browsers could be abbreviated to COFFIE. if it wasn't for IE we'd have a perfect acronym there. Darn IE messing things up again...
Ethernet Explorer ?
Internet Navigator
Safari?
COFFIES then. IE remains an offender.
COFFIES
The only places I've seen this abbreviation(and that too, mostly FF for Firefox, but FxOS for Firefox OS) is their IRC dev channels and/or mailing lists.
Ah I didn't think of the OS, that's a good point!
I've abbreviated Chrome to Ch (and Firefox to Fx).