Yes. Because the kids live with you both for the entire year, when he said you would be claiming the other child, he was treated as the custodial parent and you were treated as the non custodial parent.
He can amend his return to change this so you can then claim your child and get the EITC.
Do be aware, that if you are both claiming head of household, it could come back at you because in order to claim head of household you must pay OVER half of the cost of the home. If you are both claiming head of household for the same home you both cannot pay OVER half of the costs of the home. So be sure that you both do not say that you are.
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