Unless your dissolution judgment specifically awards your ex-husband the deduction, or you have signed IRS Form 8223 in favor of your ex, then the right to the child dependent exemption belongs to the parent with whom the child lives for more than 50% of the year.
If both parents file for the exemption, the IRS will send out an audit letter to both of you, and then you'll both get to prove your position. It appears that your ex should file a 1040X amended return, before the IRS makes the decision, because every day that passes will cost him more in penalties and interest, once things are straightened out.
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