Communication system and communication apparatus building the system

Facsimile image data received from a normal facsimile apparatus connected to a general telephone network can be transmitted as an e-mail to the e-mail address of a computer network such as a LAN or the like designated by the source facsimile apparatus. An apparatus has a LAN I/F (-) for connecting to the LAN, and a line I/F (-) for connecting to the public telephone network. Upon reception of a remote instruction from the public telephone network, a CPU (-) converts received facsimile image data into e-mail data, and transmits the converted e-mail data to the e-mail address designated by the received remote instruction.