This is not identity theft.
The parent with whom the child spent the most nights during the tax year claims the child. If there was an equal number of nights, then the parent with the highest AGI claims the child.
If a child stayed with you the most number of nights then you can amend and claim the child or both in your case. You will have to mail the amend and attach a letter explaining that the other parent claimed the children, but you were entitled to claim them.
Then the IRS will hold an examination to determine who is entitled to claim the children. You will need to prove that they lived with you using school records, doctor records. You can bring receipts for rent, clothing, and food.
Try to get written statements from teachers, coaches, even your neighbors if they have first-hand knowledge of when the child is with you.
The IRS will not care about the paperwork saying he cannot claim. As far as the IRS goes, he can claim if he is considered the custodial parent. You can claim if you are considered the custodial parent. The IRS will rule on that.
It will not happen quickly. File the amend and letter and you will be contacted someday. But the IRS has three years to conduct the examination and make their decision.
