Live Photos has expanded on your device in iOS 11. You can now take them during a FaceTime call, much in the same way you can take still images while capturing video.
Note: Both you and the recipient need to be on iOS 11, otherwise the button will be grayed out.
First, open FaceTime and start a call. If you’re in Portrait view, the button will be on the bottom left of the screen. Tap it, and your device will take a photo. A notification will let both you and the recipient know that you took it.
Now, open Photos and you’ll find a neat Live Photo of the moment, without any of the shutter buttons or options you’d usually find on the screen during a FaceTime call.
If you don’t see the button, the option may be disabled – you can turn it on or off from Settings > FaceTime.