Sending a fax is nothing else than one machine making a voice call to another and then they beep at each other. So you'd need some fax software, that knows to use the given telephony stack on the Pyra, I guess.
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While we're at it, does anyone know, what telephony stack is there with the Pyra? ofono?
In packeted real-time voice communication you rather drop a packet than having it arrive late, which is what VoIP protocols do. It makes faxing highly unreliable, though. There is or are separate protocols for Fax over IP, but at least when Telekom is involved you don't get to use that on the landline. I don't know the situation for 4G/5G or even 3G.
3G maintains a circuit switched network as I understand it, which is used primarily for voice call on that system, which the packet switched part mainly being used for data. 4G dropped the circuit switched part, so early 4G phones had to drop back to 3G to actually make a call, until VOIP was developed and rolled out for 4G networks.
I'm not sure if the Pyra's modem can be forced to drop back to 3G but I would largely suspect it's possible somehow.