She obviously likes him, because she comments on his every picture or post. She is one of his facebook groupies.
They are often unaware how embarrassing, lap doggish, or futile their behavior appears to be. While the facebook groupie is typically of the opposite sex of the target person, facebook groupies can be the same gender as the target person.
Caveat: The term facebook groupie does not extend to family members or significant others. Therefore, you cannot be a facebook groupie to your husband/wife boyfriend/girlfriend, sister, brother, cousin, etc.