Ecamm's Call Recorder for FaceTime is a Mac app that does what its name implies. The Mac OS X application records both sides of your FaceTime video calls so you can preserve your FaceTime memories. An added benefit with Call Recorder for FaceTime is that it can also handle recording for phone relay calls. This way, if you get a call on your iPhone and answer it via your Mac thanks to the relay feature of iOS and OS X, you can record audio calls that way as well.
Call Recorder adds recording controls to FaceTime on the Mac, capturing both audio and crystal clear video. It also does a great job recording Handoff Phone Relay calls via iPhones.
The app is free to try and costs $29.95 through Ecamm at the source link below.