I think I use one similar to what you are looking for that plugs into the output jack on a guitar. The one I have was an accessory for the "Rocksmith" video game on Xbox. My PC thinks it is a microphone but it inputs right into my recording software (Audacity)
What you need is a DAC, digital audio converter. There are many products out there to accomplish this task.
The important thing to remember is that DACs vary in quality. They're not all made the same and the sound quality will be different depending on the product. If you'll be using this a lot, it might be worthwhile to do research on each product and spend enough that you get something that gives you results that are worth listening to.
Mike, I do not believe that it will be as easy as that. I think that you are going to have to convert analog to digital and I think that is going to take more than just a cable, but I'm a digital dummy so will bow out of giving any advice. Good luck.
I shall post the results here, although I am not planning to go there for a while. Besides: The thrift shop is open, and I bought 2 USB mics for $1.99 each. Will now see if they work. If they do, and if there are enough USB ports on her laptop, that'll do, without a mixer or a cable.