If he did not live with the mother more than half the year, she cannot claim him. You will need to satisfy the IRS that the child did indeed live with you and not the mother for mother than half the year. I would start by calling the IRS number that should be on the notice for more information and ask what kind of proof they will accept.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**