This does not equal punitive damages. You need to contact the post office and your neighbor and have them correct the problem.
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Ms. Morecroft has given you good advice. I can only add that you could just clothespin the mail to your box, and let the postman handle it. No need to take a walk.
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You do not have to walk anywhere. You can mark the envelopes "delivered to wrong address" and put the mail in the outgoing mail box. Or, take the mail to the neighbor and let him/her know that this has been going on and he/she should speak to the postmaster at the local post office.
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