Re: Sent Litecoin to Bitcoin Address, How to recover?

For basic P2PKH addresses (Bitcoin '1', Litecoin 'L') it should be possible to recover the funds by copying the private key from the Bitcoin wallet to the Litecoin wallet.

The catch is that keys in Wallet Interchange Format (WIF) will look very different between the two networks, even though the decoded raw bytes are the same. You (or rather, the recipient, the customer) would need to export from Bitcoin, convert Bitcoin to Litecoin WIF, and import into Litecoin.

This is what the same private key looks like on both Bitcoin and Litecoin:

BITCOIN
Private key hex: 0000000000000000000000000000000000000000000000000000000000000001
Private key WIF: KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYjgd9M7rFU73sVHnoWn
Public key hex: 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
HASH160 hex: 751e76e8199196d454941c45d1b3a323f1433bd6
Address: 1BgGZ9tcN4rm9KBzDn7KprQz87SZ26SAMH

LITECOIN
Private key hex: 0000000000000000000000000000000000000000000000000000000000000001
Private key WIF: T33ydQRKp4FCW5LCLLUB7deioUMoveiwekdwUwyfRDeGZm76aUjV
Public key hex: 0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
HASH160 hex: 751e76e8199196d454941c45d1b3a323f1433bd6
Address: LVuDpNCSSj6pQ7t9Pv6d6sUkLKoqDEVUnJ

Note that only the WIF and Address fields differ, and that's only because they are in base58check format, which uses a prefix specifically for the network. Internally to each client they are using exactly the same numbers, regardless of the network.

Script for sending to Bitcoin address 1BgGZ9tcN4rm9KBzDn7KprQz87SZ26SAMH: DUP HASH160 PUSHDATA(20)[751e76e8199196d454941c45d1b3a323f1433bd6] EQUALVERIFY CHECKSIG

Script for sending to Litecoin address LVuDpNCSSj6pQ7t9Pv6d6sUkLKoqDEVUnJ: DUP HASH160 PUSHDATA(20)[751e76e8199196d454941c45d1b3a323f1433bd6] EQUALVERIFY CHECKSIG

(They're identical. Both addresses map to the hex sequence 751e76e8199196d454941c45d1b3a323f1433bd6 internally.)

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It's probably also worth considering that some of the more tech savvy customers may have already 'recovered' their funds on the Litecoin network, even after complaining to the OP and being compensated in Bitcoin.