Can my bf claim his daughter if he had her majority of the year due to court order/agreements? She has full custody and already claimed her but he should have been able 2

He had emergency custody from January until about summer, courts gave her back full custody with the agreement of him having her during the summers. So initially he had her from Jan. To September and even since then, she has only cared to take her a few times a month so he is still supporting her mostly. Mind you, she lives off the government while he is paying child support and didn't work the whole yr of 17. How is she able to claim her! Someone please help this isn't right!