If you’ve already created a custom voicemail on your iPhone, you can tap Play to see how your voicemail sounds. If you’re interested in creating a new message, tap the Custom button. From here, you can start recording your message by tapping Record and tapping Stop whenever you’re finished. Once you’re finished recording, tap on Play to make sure the message comes across as you’d like and hit Save (in the upper right) to save it as your voicemail.
Now, it’s the time for a tutorial on how to change voicemail greeting on Android. Basically, there are two methods to get it done, depending on your system operation. If you’re using Android Marshmallow, here’s what you need to do:

Besides creating an audio file in the right format (Adaptive Multi-Rate), you also need to trick the iPhone to upload your new greeting to the AT&T servers:
Of the many things your phone can do, automatically recording a phone call is not one of them. Perhaps not including that feature is a security precaution for phone makers; it could be a potential liability issue. Regardless, from time to time, documenting a call is a useful thing to do, whether you’re conducting a phone interview or cataloging a customer service call.