Do I need a phone line to receive faxes?
No, a phone is not required to send faxes from within the TTMessenger Business edition. The software is using some kind of servers to connect and send faxes like a simple email. I visited their official website and no mention of a phone requirement has been posted which means that's using the Internet to send and receive the data. You should read their description on the official website to learn more about its built-in modules and functionality.
