What's the best way to make an mp3 of an answering machine message?

Tech advice needed. I have a telephone message that has been sitting on the answering machine for better than a year, because I don’t want to delete my (now deceased) grandfather happily rambling away to wish me a happy day. I sort of fear losing the message to an accidental slip of the finger on the delete key, or maybe a power outage, so I’d like to transfer it to a more permanent and stable storage device, like my computer (as an mp3?). However, I can’t find any kind of mic or speaker jack on the phone, and the most high tech solution I can think of is to buy a tape recorder and hold it up to the phone just as if I were in high school again, recording “Wait!” by White Lion off of the radio. Is there a better way? It’s 2012. There must be. And perhaps you will tell me. Thanks!