He can ask the court to change it but the question is why would the court change it. The court will not change the right to claim the child for income taxes just because your husband wants the money.
Nope. He can try to bring you back to court to change primary managing conservatorship and possession and access so that he's the custodial parent. That's what would entitle him to that dependent deduction.
If he only has extended visitation, he is not entitled to claim that deduction. Until he actually files something, don't sweat it. If he does, consult a local attorney.
Messrs Cohan and Kielich are correct. One clarification, however may be in how the decree was reached. Parties will often agree to forego or alternate their entitlement to a tax exemption. It's unclear whether your divorce decree resulted from agreement or contested proceedeings.
It depends entirely on your divorce decree. It is not unusual for a divorce decree to have a provision that states that if the primary conservator is unemployed or unable to reap a tax benefit from claiming a deduction, that that deduction goes to the secondary conservator. My advice would be to take your decree to an attorney (or talk to the attorney who did your divorce) to get clearer guidance.
This answer is for general information only and does not establish an attorney-client relationship.
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