I'm using the wei approach (4 right-most zeros) as a marker to track user deposits on my site. In short, every user on the site is told to append a custom amount of "wei" to every deposit they wish to make so we could uniquely identify deposits from them and credit their balance. For example, User A might be told to add 36 wei (x.0000000000000000036) while User B might be told to add 546 wei (x.0000000000000000546).

Now suppose a user tries to deposit funds into his account and forgot to append his unique wei ID to the total (or worse, he mistakenly appends someone else's ID) and now wants to try to recover his "lost" funds. In order for me to override the default behavior and manually credit his account I would need to ask him for some proof that he was the sender of the funds. Normally, I can ask him to sign a message using his private key. However, the problem is that the funds were sent using a popular cryptocurrency exchange and he does not have access to the private keys. Obviously, the exchange won't let him sign a message using their private keys. I cannot refund the transaction (and let him resend with the right amount of wei) because the exchange has a policy that they do not recover refunds. Additionally, this cannot be used when the individual (claims he) mistakenly used someone else's number of wei.

What info/action can I request from the sender which would be sufficient to "prove" that he in fact sent those coins?

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