It is impossible to prove that somebody is Satoshi.
I firmly believe that even if real satoshi turned up one day, people will also declare him Faketoshi.
This is so true.
Even if Satoshi presents his privatekeys, signs messages, shows his passwords, e-mail account accesses... it could be someone else who has all these privatekeys, passwords, accesses now.
He would only prove the ownership of these but it is impossible for somebody to prove that he is Satoshi.
If we are going to find out who is Satoshi Nakomoto today or this time I time it is kinda impossible to find proof that he is the one who created bitcoin,
Anyone could claim that he is the marker of bitcoin but any documentation is impossible but in my opinion if he could have a big amount of percentage if bitcoin and he have the biggest percentage of bitcoin in here hand that could possibly be Satoshi Nakamoto since we have a theory that Satoshi Nakamoto owned a very big percentage of bitcoin and it makes sense since he is the maker or creator of bitcoin he should at least have a big amount of it since he could crack the bitcoin system.