Recording calls can get you into serious trouble unless the other party is forewarned that the call is being recorded.
There are no apps that will allow for call recording, iOS will not allow the apps access to do so.
I'm not sure that any cellular phone will allow such functionality.
Laws regarding recording calls vary from country to country and from State to State within the U.S.
He may want to look into a service like Google Voice, which has the ability to record incoming calls. It complies with U.S. laws by making an announcement that the call is being recorded and playing a tone at intervals.