How to Save or Share IPhone Voicemail Messages in IOS 9
In previous versions of iOS, saving or sending voicemail was a daunting task, but iOS 9 makes it easier by adding sharing tools.
I don’t know how long I just listened to voicemails on my iPhone before realizing that iOS 9 added a sharing sheet to the voicemail screen. Just select a message and hit the Share button to open the familiar collection of ways to save and share your voicemail. You can send it as an audio file via mail or messages, add it to notes or voice memos, or drag and drop it into third-party apps like Slack, Dropbox, or Google Drive. Quite convenient.
How to Share, Forward and Save Voice Messages on Your iPhone | WonderHowTo