No. In order to claim an exemption, the following must apply:

There must be a qualifying relationship, or the child must have lived with her for the entire year.

• Your child, stepchild, foster child, or a descendant of any of them (for example, your grandchild). (A legally adopted child is considered your child.)

• Your brother, sister, half brother, half sister, stepbrother, or stepsister.

• Your father, mother, grandparent, or other direct ancestor, but not foster parent.

• Your stepfather or stepmother.

• A son or daughter of your brother or sister.

• A son or daughter of your half brother or half sister.

• A brother or sister of your father or mother.

• Your son-in-law, daughter-in-law, father-in-law, mother-in-law, brother-in-law, or sister-in-law.

The girlfriend (if they are not married) does not have a qualifying relationship The child lived with you for 4 months (and not with her for the entire year). Therefore, the only way she could claim the exemption is if he lived with her for the entire year.