If your landline doesn’t have a way to save messages already built in, the best way to save that gorgeous message is with a recorder. But before you rush out to get it, don’t forget that most smartphones have a built in recorder. Try that first and see if it will pick up her voice loud and strong. It should save the message as an MP3 automatically, that you can send (via email or text) directly to your computer for safe keeping. If the quality is not great, then you can borrow a recorder or purchase one. We like the Olympus brand ourselves, because they save in MP3 and can upload to a computer wirelessly. We have the vtech phone/answering system indicated above. The outgoing message/greeting is of my young daughter’s voice and we would like to save it somehow. Am wondering if you have a process or can suggest how an outgoing/greeting message can be downloaded for safekeeping.
You can set when you would like to send callers to your voicemail. For example, you may want to send all calls to voicemail when you know you’re going to be out of the office and not taking phone calls. 1

You can access listen to your voicemail messages from Microsoft Teams apps or phones, Skype for Business apps or phones, or Outlook apps.
As Dan tells us, "This is the only strategy I’ve ever seen consistently work—but when they call back you'd better have a question ready!"