This guide will show you how to change the iPhone voicemail message on iOS 9. Even if you don’t use the iPhone for calls very often this is a great thing to do, since you may end up sending more calls to voicemail.
After setting the number on your voicemail, you must also record a personal voicemail greeting. Follow the steps below. Start the Phone app. if you don’t see the numeric keypad, tap “Keypad” at the bottom of the screen. Tap and hold the “1” for about two seconds until the phone automatically calls voicemail. Immediately tap “3” to access voicemail settings. Listen to the options. On most voicemail systems, tap “2” to start the process to record a new greeting. The current personal greeting will play; then tap “2” again to record a new greeting. Say the greeting you want, and tap “#” when you’re done. To save the greeting, tap “1.” The personal voicemail greeting has been set. Hangup the phone. How to setup voicemail using a Visual Voicemail Applications

This tutorial is going to show you how to record a voicemail greeting that you choose. It is a good idea to either write out or think about exactly what you are going to say before you record the message. You will then have the opportunity to play the greeting back before you set it for any incoming calls that go to voicemail.
I have the same problem. I’ve also worked with the support line (via the chat option), and have been unsuccessful at getting it set up or enabled. “The voicemail box number is invalid…”, yet, if I call my number, I can leave a voicemail, but have no way to go in and retrieve it.