The real inventor of BitCoin wrote a paper describing the architecture two years earlier under his own name, Hal Finney. He got a terminal diagnosis of ALS a few months before he launched the BitCoin service, the pseudonym being necessary at the time because of the Haber-Stornetta patent on the BlockChain.
No, Hal, did not keep the coins. He invented BitCoin because he was a crank with weird ideas about inflation, not to get rich. Mining the coins and keeping them would have been a betrayal of his principles.
The proof of this is given by the fact that Hal did not in fact get rich from BTC despite being the ''second' person to join the project. Nor did Hal ever complain that Satoshi took the credit for what was very clearly his work. If Hal had been just another person coming along, there would have been every reason to keep the cash.
And we do in fact know Hal ran mining servers from the start and that he ended up in serious financial trouble due to his ALS. The freezing his head thing came from donations.
Craig Wright does seem to be the last of the three early advocates alive but that doesn't make him Satoshi. Wright has never shown the slightest sign of being the sort of person who builds such a thing and in any case, Hal's name is on the much earlier paper.