My son recently bought a house with a large walnut tree in the garden. Should he leave them on the tree to ripen or pick them when green and ripen in doors.

Best to leave them till the green cases turn brown and start ot split open naturally. They can be harvested off the tree when ripe, but tend to fall to the ground anyway.
One downside is the cases and the the lining that enclosed the nut tends to be black and 'slimy'. It will stain thigs so its best to wear gloves, pick them up and leave them some where warm to dry the slimy 'stringy' bits (for want of a better word) up!

Leave them on the tree Kerri, they will be ripe when they fall, although the squirels like them too.

Sorry Nicky posted at the same time.

a m8 has one and I go round every year about late october onwards and collect them, always manage to get loads as no-one else eats them but I love them.

Great minds Doc!
If he has squirrels, then i doubt they will leave any form him, just bury aorund garden in pots and beds, ready to germinate in spring! A friend has a huge walnut and the squirrels do this, they also throw them at her! not joking!