Does Windows Explorer “see” the files like a disc drive? If so what format are they?
If you can’t read the files (of they are in an odd format and you can’t open them) you can re-record the audio from the headphone jack. The only catch is, you need a soundcard or an audio interface with line inputs. (Most laptops have only mic-in and headphone-out.)
The Behringer UCA202 or UCA222 is an inexpensive USB audio interface with line inputs, but current reports indicate it’s in short-supply. There are lots of higher-end interfaces with switchable mic/line inputs. If you buy an interface, be sure to get an appropriate cable/adapter. Do NOT buy a regular “USB soundcard” because they are like laptops with only mic-in and headphone-out.)
One more thing - - I take it the regular mic-in connection on my PC isn’t good enough, right?
Right. It can “work” but a headphone or line level signal is about 100 times stronger than a mic signal so the mic input is too sensitive (and often low quality). And, if you have a mic+headphone combo jack it takes a special 4-conductor TRRS plug to make the microphone connection.