For a signature, or to “move his stash” as you said? The Genesis coinbase itself can’t be moved; it is not sent to that address, but rather, in P2PK to a public key that people convert to that P2PKH address as an anachronism.
18.53375545 BTC (as of writing) from that address can be moved, if you have the wallet (private key) of Satoshi.
The correct (movable) amount is listed by Block Stream Explorer (note how the 50 BTC mining reward transaction is not listed here for the same address):
https://blockstream.info/address/1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNaI almost said as much, but then cut it as an unnecessary tangent. I
try to prevent my posts from being too long.
If I know that people are converting the Genesis coinbase P2PK key to a P2PKH address (an arcane detail that few realize), I obviously know that idiots have been sending money there, and how much of it. Should I now embark on the tangent I had in mind about why that’s a bad idea?
The point from which I do not want to distract with this tangent:
Moving money around not the right way to ask Satoshi to prove his identity. signmessage exists, and it works. Satoshi has a PGP key; I linked to this forum’s copy of it, and I provided the fingerprint. The
threshold test for any Satoshi claimant is to sign an appropriate message with a known Satoshi key.