Recent updates to the stock Android Dialer app have brought the ability to share voicemail with the addition of a Send To menu option when viewing a voicemail.
Many may not initially notice the option to share if they rely solely on the voicemail transcription feature as the option does not appear until you actually listen to the voicemail. Once you listen, the send to option appears at the bottom of the menu as seen to in the image on the right.
Once you tap the Send To option, you get the standard sharing options including recent emails, and recent Google Drive folders. In addition you are presented with the email application options you have on your device, Save to Drive and Android Beam to magically send to another nearby Android device.
Please note, there are some issues with sharing voicemail at this time. Currently the file genereated does not have a file type associated with it, so there is nothing to open it with. However, if you rename the file with a suffix such as .MP3 you will then be able to open the file.
This is a nice option if you ever need to send a voicemail to someone else or you just want to back up a voicemail for safe keeping.