What should I do if someone else claims an award that I actually won? I am a PhD student. A few years ago, I won the best paper award at a conference.
However, they didn't post the list of winners on the conference website.
But when I google the name of the conference, the very first search results include someone who already graduated and claims on his personal webpage and LinkedIn profile that he won that award.
The only proofs that I have are the award itself and a congratulation email from the committee.

Currently he works at a company so I don't know how to handle this case especially after his graduation he may no longer care about consequences.

What can I do in this situation?
Send him a message

Even if you think you know the only truth, maybe there is something you don't know about this award.
If there is no response in.. let's say 48 hours, let's go to phase 2

EDIT : concerning the timing, @O.R.Mapper is right, if he is on a vacation... bad luck.

Send a message to the committee 

They gave the award, so explain the situation, and ask them to put on their website the name of the winner for each year.
Explain why you want this.

If the commitee is reacting (if not, will be hard :/)

Send a (still) polite mail to the cuprit and tell him he MUST remove what he puts online.
No response ? let's go to the last part

Write to his university

Even if you think they might not care, it's still a graduate student, it's bad for the reputation of the university to have graduate student with a bad behaviors.

EDIT : as said by @CaptainEmacs , do NOT to accuse someone, even if you're sure it is the truth. Tell politely that you think he might have mistaken, that is all.

I think that's the proper way to do it.