Fan favourite Sonny Bill gets new medal
The boy, identified as 15-year-old Charlie Lines, was thrown to the ground by a security official after running on to the Twickenham pitch following New Zealand's 34-17 triumph.
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"I am sure that he'll remember it. I'm happy that he has it because I know that he will really appreciate it," Williams said at Sunday's World Player of the Year awards.
"When he's older, he can tell the story to his children."
The 30-year-old Williams played down the incident which also saw teammate and flank Liam Messam give the teenager his black beanie hat.
"I'm really surprised, most of the boys would have done the same," Williams said.
Agence France-Presse