My husband didnt have the dependency of this child but is leaving w/ us amlost all year?

My husbands son is living with us almost all year with the exemption of every other weekend and half of the summer vacation he goes to his mom. But the divorce decree awarded the ex wife to claim him. I have been reading and ask question last year about child tax credit and my husband cannot claim him bec he is not my husbands dependent but i believed my husband can claim him for EIC,am i right about this? And im not sure how much we can get back from claiming him in our EIC and my husband never claim him in EIC since the final divorce date.If so can he is entitled to file for EIC with this child who is not a dependent but lives w us will he be able to file from those previous years that he didnt do EIC?????