Give him a signed Form 8332 to allow a non-custodial parent to claim the dependency and child tax credit. You as the custodial parent can still claim child care credit, EIC and file as head of household if otherwise qualified to do so.
"Fully"? The child must live in his home more than half the nights of the year.
If not, only the parent where the child lives more than half the nights can claim the child as a dependent. If that is you, you can give your ex a form 8332 dependent release form, which will allow your ex to claim the child tax credit. But EIC, qualification for head of household, and the dependent care credit, always stay with the custodial parent and can never be waived, transferred or given away.
Alternatively, you lie and say the child lived with your ex more than half the year, and you don't claim the child at all. If you get caught, you can both be penalized, including automatic disbarment from EIC for a minimum of 2 years.