It’s kind of a mess. He would have to wait until his tax liability is settled and then amend his return which will take 6-9 months to process. You will have to mail your return with an explanation that you can claim your dependent and that he is amending his return accordingly.
An easier way is for you not to claim the child this year. You could claim the child in the next 2 years to compensate if you do the dependency on alternate years. Or he could pay you for the amount you are losing by not claiming the dependency this year.
Also keep in mind that if you are the custodial parent even if he claims the dependency you can still on your return claim the EIC and child care credit as well as file as Head of Household if otherwise qualified. In addition, if you are the custodial parent you would have to give him permission to claim the child by giving him a signed form 8332.
