If you have any program that can play the apple songs, you could try re-recording them with another program while they're playing, ("loopback" style).
If you've got some pulseaudio packages installed (pulseaudio-utils) you could use
pacmd list-source
to find your output device - it's usually the one with ".monitor" at the end of it's "name:" entry.
Then, record it's output to a file using parec and it's --file-format[=FORMAT] option. Check with --list-file-formats & see man parec ("It understands all audio file formats supported by libsndfile.") Something like this:
parec -d alsa_output.pci-...analog-stereo.monitor --file-format=wav output.wav
Or pipe to lame to record mp3's:
parec -d alsa_output.pci-...analog-stereo.monitor | lame -r -V0 - output.mp3
-r tells lame that the input is raw pcm.
- tells lame to input from stdin
-V0 says "Enable VBR (Variable BitRate) and specifies the value of VBR quality (default = 4). 0 = highest quality."
The only tricky part is getting the timing of each song & output file. If your Apple playback program supports terminal playback that would be easier, you might even be able to combine ID3 tag reading to transfer some data (if the Apple files support it, I'm not actually sure)
You could also use another GUI program called audio-recorder, it's basically "click to record", and then convert to mp3.
Or even audacity and some GUI pavucontrol software if you really wanted. See this Ubuntu Q on How to record output to speakers?.