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Dear JACUSTOMER - I would agree that you have the "upper hand" assuming this is a valid debt. I can only tell you from a legal standpoint what rights you have in this situation and only you can make a decision as to what is good for your business. The customer would have no legal basis to reduce the amount unilaterally so unless there is a "meeting of the minds" as to some settlement amount you have the right to demand full payment.
Obviously you don't want to lose your best customer however the flip side is the question of "who is running your business - the customer or you?" So you are negotiating from a position of legal strength but you are the only one who can decide how much you want to ask of your customer without taking the risk of losing the customer.