File started: 7:19 AM 2/7/2017

I tried these steps on both the iPhone 5C with IOS 10.2, and the iPhone SE, with IOS 9.3.
Note: Available options will vary depending on installed apps.

If you want to save voice mail messages stored on your iPhone to your computer,
the following steps should work:
1. Open the phone app, and select the Voice Mail tab.
2. In the list of messages, select the sender's name for the message you want, and double-tap it.
3. On the resulting screen, move to the " Share" button, and double-tap it.
4. On the resulting screen, flick to the right to move through the available options, and then double-tap the one you want, to move a copy of the message.
5. What appears on the resulting screen will depend on your choice, as follows:
Air-Drop recipient, will allow you to share with someone in your list.

Mail, will open the mail app to send the audio message as an attachment

Message, will open the message app to send the audio message with a text message.

Voice Memos, will place a copy of the audio message in your voice memos app, and if configured properly, 
should copy the message to your iTunes media folder when you sinc your phone with iTunes on your computer.

Dropbox, will open the Dropbox app to save a copy of the audio message there, and likewise will copy it to any devices you are sharing with your Dropbox account.
When choosing this option, you will be placed in the Dropbox app and will need to double-tap the "save" button to complete the task.

Note: If you choose the "Voice Memos" option, double-tapping on it once will complete the task and return you to the original screen on the Voice Mail tab.
