If you were Satoshi, what would be the benefit of claiming that in public (think it through at least twice before replying)? When someone gives a reasonable answer to that question it might be worth at least put their claims to test, which is pretty simple, just move Satoshi's stash of BTC, end of story.
If by “Satoshi’s stash of BTC”, you refer to some huge amount, then you are referring to the so-called “Patoshi” coins. Nobody knows if those are Satoshi’s; I tend to think not. It can’t be proved either way, unless Satoshi or Patoshi steps forward.
The threshold test for anyone who claims to be Satoshi is
authentication with a digital signature from one of Satoshi’s known keys: His PGP key, or the key for one of the Bitcoin addresses definitively known to be Satoshi’s. Not moving coins that may or may not be Satoshi’s, and that may coincidentally move while some random scammer claims they did it.
I don’t ask someone’s motives before
demanding that. If the claimant refuses (as Craig Wright has), then his motives are obvious: He is an imposter.