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If you have a visual voicemail from FaceTime you want to preserve, you can save it with the Files app:

While missed calls aren’t ideal, you can let your caller know you’re still there for them by having a great voicemail greeting. The best business voicemail greetings let your customers (and potential customers) know why you’re not available and how they can best get in contact with your business. They are also short and to the point. You usually want to keep your greeting between 6 and 24 seconds long so callers don’t hang up halfway through.
On the home screen, expand the App Drawer and tap on the entry named Visual Voice Mail. You’ll be taken through some introductions screens that will showcase some of the capabilities of Visual Voicemail. Tap on Start to configure the service.If you’re a new customer or you haven’t gotten around initializing your voicemail, you will be prompted to do so. But if you followed the first guide, that won’t happen. In any case, after you enter your voicemail password, tap on End Call. After a short waiting period, your Visual Voicemail should now be configured. From the next screen, you can Set your personal greeting or hit Ok to skip this step. To check a voicemail with this service, open the App drawer from your home screen and tap on Visual Voicemail.You’ll see a list with all your voicemails. You can select them All or tap the New tab to only display the ones that you haven’t listen to so far. After you open a voicemail, you can listen to it by tapping the Play icon. To delete a message, tap the trash icon then tap Delete.