There are paid options on Google Play for sending and possibly receiving facsimile transmittals through third party services.
There ought to be an open source app capable of placing a call directly to a fax machine and using a software-modulated audio signal to directly transmit the fax from the cell phone.
Or answering a call on the cell phone from a fax machine and receiving and demodulating a facsimile transmittal and saving it as a pdf file.
I am not sure if that can be made to work acceptably. GSM fax gateways don’t work that way, they use GSM data call functionality instead. I don’t think Android offers any way for apps to place data calls.
I am not sure either. What baud rate cell phone voice call transmissions are capable of, TDD or TTY calls in addition to fax. But with better audio quality on 4G, 5G networks etc., it should be possible.
But no, and the answer is absolutely no, h311 no. Voice band is very harshly restricted to voice only. If FAX or TTY or TDD is detected, a strong interference comes online to prevent any known sort of data connection from being established.
Businesses pay a lot of money for fax lines and if a fax is detected on a line not specifically authorized for fax transmittals, it is immediately cut off. I don’t believe it’s an actual FCC rule, but it’s enforced as if it were nonetheless.
Telco guys have always been best of buddies with government regulators, NSA spies, local cops with wiretap access etc. I’m not privy to any of that stuff obviously, but those guys are anal, and everything not specifically authorized by them is prohibited.
In germany every fixed line was capable of fax until the net got digital. Now I don’t know but I never heard of such a thing.
Image transfer via audio like hams do it is not helpful to you, is it?