to claim a foster child as a qualifying child, the child must be with you by an authorized placement agency or by judgment, decree, or other order of any court of competent jurisdiction. this would satisfy the relationship test    and having the child for over 6 months would satisfy the residency test .

when something like this happens your only option is to paper file. 

Eventually, the IRS will send each of you a notice asking you to amend. If no one does, the IRS will send another notice asking each of you to provide proof. The one with the better proof gets it and the other gets a tax bill.