First of all, this is not an advisable thing to do. Because you can’t record your screen natively on your iPhone anyway, you’ll need a Mac in order to accomplish this. However, if you insist on saving a FaceTime call on your iPhone using your Mac, here are the steps you need to do.
Saving a FaceTime Call on Your iPhone Using Your Mac
STEP 1: Connect your iPhone or iPad to your Mac with a Lightning cable or 30-pin connector.
STEP 2: Open QuickTime on your Mac from your dock or Applications folder.
STEP 3: Click File in the Menu bar.
STEP 4: Select New Movie Recording.
STEP 5: Click the arrow next to the record button in the QuickTime window.
STEP 6: Choose your iPhone from the list of available cameras.
STEP 7: Unlock your iPhone; it’s display should now appear in QuickTime on your Mac.
STEP 8: In QuickTime for Mac, make sure that the volume bar is turned up. Otherwise, you won’t be able to hear your call, and what would even be the point of having it?
STEP 9: Open FaceTime on your iPhone.
STEP 10: Click the record button in QuickTime on your Mac.
STEP 11: Place your FaceTime call on your iPhone.
STEP 12: Click the stop button in QuickTime to stop recording when you’ve finished your call.
STEP 13: Click on File in the Menu bar, then click Save.
STEP 14: Give your recording a name, then select the location where you want to save it.
STEP 15: Finally, click the Save button.