You will be asked to delete your current Voicemail greeting. Click on the ‘Yes’ button that appears on the screen if you want to remove that. You can save your new recorded Voicemail greeting or can use the default recorded option. Wait and hear the new Voicemail greeting message that the instructions speak out. If you want to keep that recording as your Voicemail greeting, then save it. Or you can re-record the message to get a different greeting.
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.

1. Some mobile phones have a Voicemail app easily accessible from the get-go. To start the voicemail setup process, just tap on the Voicemail app and follow the on-screen prompts.
To set up Visual Voicemail, tap Set Up Now. You’ll be prompted to enter and confirm a voicemail password. Next, you’ll have the option to choose the default voicemail greeting or record your own. If you want to record your own custom greeting, tap Custom. Once you’ve entered created your password and chosen your greeting, you’ll be able to receive voicemails and view them in the Phone app.