I sent someone Bitcoin but they said they didn't receive it because their phone is powered off but I got a complete transaction confirmation
The recipient doesn't need to have a wallet online to receive Bitcoins.
This is because the transfer of the money is recorded in the blockchain - which every full node (wallets etc) worldwide has a copy of.
Bitcoin wallets don't actually contain money. So they don't literally receive money. The only really important data in a wallet is the secret number known as a private key.
You should first check on the transaction (tx) id generated when you sent the funds and then check it on any btc explorer (https://btc.com/) to confirm that it was sent and how many confirmations.
You should use that as a proof that your funds were sent properly.