well, you always have the option of telling the customer that if he won't provide the information, you won't cash the check. Having the information is for your benefit, not his. If the item is returned (your customer gets his statement and claims fraudulent, altered, forgery, etc.), how will you get in touch with this person? You won't, and will be stuck with the item.
Hussam - thumbprints don't really work as a method of identifying customers after the fact.
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Providing alternative truths since the invention of time