I finally got it back (yey!), so for people with the same problem, here the different solutions:
Ask them to send it directly to you: Work only if you have a friend or an adress in Japan. They refuse to send it outside of Japan.
Using a janapese package forwarding service (see fkraiem comment) to send you the item: It may work if the item is still in the lost&found of the Tokyo Japan Rail (they keep it 3 days). You have to ask the JR to send the item to the shiping company so that they can send it to you. Beware that as people have noted in the comment they may not accept to send a phone because of the lithium batteries, but most of the time it should be fine.
This does NOT work if the item is in the police station, because they will charge a fee for sending it and shiping company doesn't accept to pay fee (even if you want to pay them for that also). (I am not sure if the JR L&F ask for a fee!)
Finding somebody in Japan ready to send it to you: OK, but you have to trust someone you may not know. Can still be ok because Japan.
At the end I found a collegue working in Japan who manage to recover my phone from the police station and bring it back to me.
- The lost&found JR office keep the item 3 days before sending it to the police.
- The police station keep it 3 month before destroying it.
- The police station ask a lot of informations to identify the phone as mine, despite the fact that the lost&found JR office recognize it before and give a special item number to me. For example, they asked me:
- A letter of attorney
- Phone color and brand of the phone and phone shell, plus other visual informations.
- PIN number (hard to know if you didn't record it before, so I end up giving my colleague the locking pattern).
- You may need to ask your friend to bring a cable to charge the phone.
It has been a long way for me, my colleague call the police station 3 times to be sure to have all the documents, I hope this will helps!