On the iPhone, go into voicemail and tap "Greeting". Record a few seconds of something and tap stop. Before you tap save, use iFuntastic or SFTP to navigate to /var/root/Library/Voicemail on your iPhone. You'll see a file called "Greeting. amr". This is the audio you just recorded. Delete that file and replace it with your custom message which should then be renamed to "Greeting.amr". Tap "Play" on the iPhone to verify your message works. If it plays, tap "Save" and your custom message will be uploaded to AT&T's servers.
This article shows you how to save voicemail from iPhone, and export them as audio files to computer in the easiest way.

Android phones can access voicemail by holding down the 1 key on the dial pad until the phone dials your 10-digit phone number. You will automatically connect to your mailbox and be prompted to enter your temporary password; this password is the last 4 digits of your phone number followed by the # key. Start the Google Voice app. Tap the three horizontal lines at the top left of the screen (sometimes called a hamburger menu), and then tap “Settings.” In the Voicemail section, tap “Voicemail greeting.” Tap “Record a greeting.” How do I access my voicemail? To call your voicemail on an Android phone, simply open your phone’s dial pad and hold your finger down on the “1” key. You can also call your voicemail from a different phone by calling your own number and tapping the pound key. How do you check your voicemail?
Tripboba.com - Voicemail is a voice message that a caller will leave to your mailbox when you’re absent or busy with another conversation. The same goes if you’re trying to call someone else and they don’t answer. You can leave a voice message and they will receive the mail, allowing them to hear what you want to say.