What you're proposing is losing the digital quality through a double conversion from digital to analog (A/D), patching jacks with an analog audio cable, and then having the PC convert analog back to digital (D/A), not an uncommon practice, but both conversion stages add extra noise and so deteriorate your S/N signal to noise ration.
A couple of critical pieces of audio electronics info that most people don't know is that MIC inputs (similar to phonograph inputs and sources) are not electrically compatible (do to impedance mismatching) with other audio levels such as headphones (preamplified output) or the most common line level signals, e.g. you have with PC audio line outs, audio amp inputs, VCR, DVD, Tape, DVR, videocam audio, etc. etc.
So trying to patch headphone out signal (already converted to an analog signal) into any Mic level jack most often gives you very high distortion and/or low volume, at best, and maybe no sound or horrible screeching noise, in worse case scenarios. That being said, there are fancy technical solutions, using active or passive impedance matching circuitry etc. but you'd need to consult an audio technician or electronics hobbyist guru to get that sort of thing working for you.
The less sophisticated, and less expensive, but easier solution if you need to archive the stuff and regain memory storage in your digital recorder, is to use standard old magnetic casette tapes and casette recorder and run your analog Low level headphone jack signal either through a preamp (if needed) then the preamp outs into the Line Level inputs on the tape recorder, or else if the signal input to the tape inputs is registering hot enough on the input level LEDs or old analog needle meters, then you can omit the preamp and go directly into the tapes inputs, relying on its internal preamps. In either of these setups it's analog all the way from the headphone jack to the tape, with no intermediate D/A/D conversions to degrade the signals.
Yeah, it's ol' skool, and not a digital solution, but wattaya gonna do?
If you had a more expensive modern digital recorder, e.g. the pro, or semi-pro consumer model decks, they would give you digital output as either digital coax, or (even better) the S/PDIF fiber optic digital audio outputs, or both, e.g. you can commonly find on newer DVD players and DVR decks. Of course the target has to also have the appropriate matching inputs. My AV receiver has 3 of the optical audio ports, but no coax, so I selected my other components accordingly. Other units have only the digital coax audio I/O and so can not make use of optical audio cables or sources.
If, like me, the unit with the content on it, that you are referring to is one of the affordable minature hand-held pocket size digital memo voice recorders, your only other option is to let it playback out its little speaker placed near a microphone plugged into your PCs audio mic input jack and record it accoustically (open air) but that will also introduce ambient noise.