An information processing apparatus capable of reliably switching a session. An IP fax as an information processing apparatus is connected to another IP fax. The IP fax establishes an audio session with the other IP fax. After establishing the audio session, the IP fax receives capability information indicating capabilities of the other IP fax therefrom. After receiving the capability information, the IP fax requests the other IP fax to switch the audio session to a T.38 session. Then, the IP fax switches the audio session to the T.38 session.