Communication apparatus, method of controlling the same and storage medium

A non-transitory computer-readable storage medium storing a program for causing a computer to function as a communication apparatus comprising:

• a modem configured to perform FAX communication;
• a connection unit configured to connect a telephone apparatus;
• a detection unit configured to detect a CNG signal;
• and
• a control unit configured to control so that in a case where there is an incoming call in a state in which the FAX communication is being performed by the modem, if the CNG signal is not detected by the detection unit, a signal is supplied from a line to the telephone apparatus, and to control so that in a case where there is an incoming call in a state in which the FAX communication is not being performed by the modem, if the CNG signal is detected by the detection unit, FAX communication by the modem is initiated.