If the thief opens his wallet and gives OP an address, and OP sends 10,000 sats to that address, the thief's wallet will show the incoming transaction within two or three seconds. You can test this yourself when you pay for something using a payment processor, which detects your transaction seconds after you hit send. You can even test this yourself by opening two Electrum wallets and sending coins between them. As soon as the transaction is broadcast, it is relayed across the network within a few seconds.
Uhm... maybe this is the case with Electrum and / or some other wallets... But this doesn't happen with
all the wallets. I can confirm you that Bitcoin Wallet for Android and Jaxx don't list a transaction with 0 confirmations. And, most likely, other wallets do the same.
This transaction, as example:
https://blockchair.com/bitcoin/transaction/abb0a820a43e92ff9e3a1f9e6967f2c59e76b5cd1909d44c06af813e75251913Was sent to my address from Bitcoin Wallet for Android
4 days ago and it still has 0 confirmations. And it still doesn't appear in my wallet. If you wish, I can also upload a screenshot from my wallet...