Fax connections over GSM required a special (read: expensive and inefficient) circuit-switched data service that was limited to 9600 bps, at least here in the U.S.A.:
Same in Europe, HSCSD and all. Though at the time, I thought my Nokia 6150 was really "modem'ing" and the 9.6kbps were because GSM compression and available bandwidth would obliterate anything else, but nice to learn after all these years that it was actually digital and the endpoint with the actual modem was somewhere in the network.
The way this would work is that your cellphone would send the fax data over the digital cellular network connection; in turn, the actual cellular network itself would speak the V.29 fax protocol.
People say this all the time on the internet, but in the 90's, I had a Nokia phone that could send faxes over GSM.