There is a way for you to allow another to claim a child if both parties have paid for at least ten percent of the support of the child during the year by using Form 2120
If he does not pay for any of your granddaughter's support and you provide for all of her support, there is not a way to allow him to claim her on his tax return for the year.
So, if he can pay for at least 10% of her support you can use Form 2120. For more information see Multiple Support Agreement in Publication 501.
I hope this helps explain the tax rules that could allow for another to claim your granddaughter that lived with you (even though I can not guarantee that will be enough for her to claim residency for tuition after she moves).
Best wishes and bless you for caring for your grand daughter.