Every signed transaction hashes to a unique identifier. Wallets show it after sending, and a block-explorer resolves it to the full detail: sender, recipient, amount, fee, and whether it succeeded or reverted.
When support asks for proof of a deposit, the txid is the proof. It is also how you check whether a transaction failed on-chain, which matters because a failed transaction still consumes gas and still uses up its nonce.
Practical habit: before contacting an exchange about a missing deposit, open the txid yourself. Most "missing" deposits are either unconfirmed, sent on the wrong network, or sent to a contract address that cannot credit them.
Related: block-explorer, confirmation, failed-transaction, crypto-address