Once recording is completed, hit Tap to stop recording. Your recording will be saved and displayed as Custom greeting. To listen to your greeting press Play button.
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.

From the Skype for Business desktop app (if you are running Click-2-Run build C2R 8201.1002 or later), select Set Up Voice Mail. Change your Call Answering Rules You can change what options your callers have when they reach the voicemail service; get disconnected, hear your greeting, record a message, choose to be transferred to the number or user you select. Change your prompt language This is the prompt language that is played to callers. For list of supported languages, see Languages for voicemail greetings and messages from Skype for Business. Configure your Out of Office greeting This is the customized greeting message that is played to callers when your status is Out of Office. This option can be activated "Always," when you have an active "Auto Reply" in Outlook, or whenever you have an out-of-office calendar appointment.  Where you can get your voicemail messages from
Open your device’s Phone app ​.At the top right, tap More .Tap Settings. Voicemail.You can: Change what handles your voicemails: Tap Advanced Service. Set up your voice mailbox: Tap Advanced Setup. Change your notification settings: Tap Notifications.