I know it is low tech, however a few years back I transferred some tapes I had (comedy, Jeff Foxworthy, etc.) to my computer.
What I did is take my home stereo system, made me a patch cord from two old sets of headphones (cut about two foot of cord of each, then spliced them together, so that I had a headphone jack on both ends--you can buy this too, but 7 or so dollars for something I could make from old non-working headphones wasn't worth it too me). Plugged one into my mic-in on my computer and the other in the headphone jack on my stereo. Played the tapes on stereo as I recorded them onto MP3's on my computer using a freeware program called StepVoice Recorder.
StepVoice Recorder | Download version 1.4 is newest, they have 1.5 BETA though.
It allows you to set up for either mic-in or line-in, along with recording what you play on your computer. Just have to set volume on record player to right amount (not too loud and not to low) so that recording will have good audio (if audio coming in is too loud, it will be distorted, if it is too quite, you won't be able to hear it over the background noise, especially LP's). Once transfer is complete, you can burn MP3's to CD's as MP3, or you can make a CD from MP3 files (a lot of CD player won't play MP3's, but if your friend has one that will, you can store a lot more on a MP3 CD than you can a plain old CD). The only negative is if you record an entire record into a single MP3, you'll have one really long track. So you can either pause playback and recording and make multiple MP3's (stop playback and recording, start recording to different MP3 and start playback and repeat every 4 or 5 minutes). Or you can use what I used, another freeware program called mp3directcut found at
mpesch3.de - Homepage of mp3DirectCut and 1by1 - free mp3 editor+recorder and audio directory player so that you can take long MP3s and divide them up into smaller MP3's and therefore when you record to CD, you'll have multiple tracks, instead of one big one (five different MP3's recorded to CD will be 5 tracks on CD). This software allows you to listen to playback of MP3s, and therefore allows you to choose when to cut it (your friend gets to choose where each track is).
Like I said, low-tech, but it worked for me. The tapes I had were owned by me, and since I didn't have a tape player in my car, I wanted to listen to them, and it worked out great.
If your friend don't have mic out on record player, you can either set up a very quite room and a mic to record LP's or you could use some old speaker wire for left and right speaker combined into single plug to be plugged into microphone jack on computer. Just make sure you don't turn volume up real high.