No, he can't. You are not a blood relative, so one of the rules is that the dependent must have lived with you the entire year. There are two types of dependents for tax purposes: qualifying children and qualifying relatives. Your step-daughter is not a qualifying child because she is not a blood relative. To claim a dependency exemption under qualifying relative rules, she must have lived with you for the entire year.
Form 8332, referenced by
@TurboTaxColeen only provides for the release of the exemption to the noncustodial parent of the child - not a non-relative.
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