Transfer iPhone 5S music to iPod Shuffle gen 2 from iPhone backup

I need help figuring out how to restore an old iPod Shuffle gen 2 with songs from a backup of an iPhone. I have my own laptop with my iTunes account and my own iPhone backup on it with my songs and such in that iTunes account. My son, who doesn't have a laptop, wants to share songs from his iPhone to this iPod Shuffle gen 2, so I backed up his iPhone to my iTunes account and tried, unsuccessfully, to restore the gen 2 iPod shuffle with the backup of his phone. How else can we move songs from his iPhone to the iPod via my computer that only shows my music in the iTunes software?