That might depend on the details if the old voicemail system. You didn't tell about that.
How about simply recording it with a microphone?
Hi everyone, I have a family member who has had cancer and her voice is stored on our home voicemail, we would really like to keep it but the phones aren't working anymore, we could get new phones but want to be able to migrate her voice so that we still hear it when we call home, does anyone have advice on how to migrate this voicemail message to a new phone system? Thank you so much!

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