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The Rule 9 under EIC and divorced parents answers the question.
Applying Rule 9 to divorced or separated parents or parents who live apart. If a child is treated as the qualifying child of the noncustodial parent under the special rule described for children of divorced or separated parents or parents who live apart, only the noncustodial parent can claim an exemption and the child tax credit for the child. However, the custodial parent, if eligible, or another eligible taxpayer can claim the child as a qualifying child for the EIC and other tax benefits. If the child is the qualifying child of more than one person for these benefits, then the tiebreaker rules determine which person can treat the child as a qualifying child for EIC.
If the parents do not live together, then the custodial parent may claim the EIC on the child that is not their dependent. The child must live with the parent that claims them for EIC purposes.
See the instructions for EIC page 2 of EIC Form;