One solid evidence would be: showing Wallet A's master public key. But that involves showing all of your wallet's addresses and transactions.

By giving it to someone who knows Bitcoin, it will be possible to show that the change (UTXO) from that particular transaction was the one sent to WalletB because they were derived from the same SEED.
If the wallet isn't HD (Hierarchical Deterministic) or the used change address was just imported, this can't be used because anyone can just "import private key" to add the address to the wallet.

Providing the transaction ID alone isn't that solid IMO, it's too easy "fake" the change address by using "coin control" or "pay to many" option/command.