There is no reason to do this and you don't have to send them any proofs, everything they need is already on the blockchain.
I thought it would help a little. While we can't identify the root cause of this, although I'm leaning it's a system error they somehow can't reflect the incoming txid to the user's account (whether it's related to an account exception the OP may have had in the past so the restore wasn't done properly). What I saw on txid, it was OP's 1st deposit, which was then swept to a hot wallet 1 hour later.
But I'm also not going to discount impersonation scenarios (as I described earlier).