There are CD burners that hook up to your stereo -- you could record the LPs directly to CD, then have your grandson rip the songs (and fix up the tracks -- the CD player is hit and miss when it comes to separating the songs into tracks).

Also, many computers have mic in or line in -- you could go from the record player through a receiver or pre-amp (or some way to get the phono out to be properly matched with a line in) and capture wave files on the computer, then convert to MP3.

There are probably other solutions too. My second suggestion would be cheaper than the first, if you already have a computer that has the right inputs.