I changed my mind, and want to retract what I said that   Craig Wright may indeed be Satoshi Nakamoto. Instead I say that I believe it is not very likely that he is Nakamoto or part of the team behind Nakamoto (but cannot exclude it). The reason is that I since discovered the following news article

https://www.coindesk.com/policy/2022/09/15/craig-wright-tells-court-he-stomped-on-the-hard-drive-containing-satoshi-wallet-keys/

that Craig Wright states that he destroyed the keys. That doesn't sound very probable to me, that somebody destroys the keys to this huge amount of money.

I still think what I brought up is an interesting twist to the story: Craig Wright pretended to have signed a message with the keys from Nakamoto (and if I understand the reports correctly this was fake, by misspelling the word "signature") , and the message essentially says "I don't sign this message as Nakamoto".  And nobody seems to notice this. This is definitely clever. It doesn't mean that I admire him as a person, but it is interesting how he was thinking ahead of what might happen like a good chess player.

What is interesting is that in the Norwegian court case he said he destroyed the keys in May 2016, and in the video posted on 5 July 2017 he at least gave to me the impression as if he claims to have the keys. But there might be a different explanation.

What I wrote above is carefully formulated, I don't want to get into a legal battle with Craig Wright.

Everybody believed that when Craig Wright made his wrong cryptographic proof he was cheating. But this was a deliberate hoax, making a fool of us all.

The video 
https://www.youtube.com/watch?v=FIvqn87iAz8 
reveals it all (but apparently nobody understood what he was saying):

One needs to look at the message he claimed to sign but didn't sign:

"  Wright, it is not the same as if I sign Craig Wright, Satoshi.\n\n"

which was a variant of the message by Sartre by which he refused to take the Nobel prize:

It is not the same thing if I sign Jean-Paul Sartre or if I sign Jean-Paul
Sartre, Nobel Prize winner. A writer must refuse to allow himself to be
 transformed into an institution, even if it takes place in the most honorable form."

So in essence he was a saying: If I sign the message that I'm Satoshi, then I betray myself because then I'm no longer the person I was before. I refuse to sign.

So he didn't cheat because he didn't have a key, but because it is against his anti-authoritarian conviction.

This doesn't prove of course that he has the keys, and doesn't prove that he is Satoshi Nakamoto, but for me the mindset this is coming might indicate he may indeed be Satoshi Nakamoto.