O.O.
Gonna go with my original answer:
Yes.
But please only try the shampoo on his head, don't steam clean it!
(Sorry, couldn't resist!😛--again!)
Is it oil from his head or product he uses on his hair?
I'd probably try anything & everything to see what works. Because stained, it's ruined.
If you ruin it with cleaners? Get a wooden headboard!