Here are the proper uses of those grammatical forms:
USAGE OF THE PERFECT INFINITIVE “TO HAVE BEEN”:The perfect infinitive “to have been” is used (1) as a noun form to denote a hypothetical state or condition in the past, or (2) as a noun form to denote a previous state or action that is no longer subsisting.
Usage 1. As noun form to denote a hypothetical state or condition in the past, or a state or condition in the past that has been determined to be true only now:1. “
To have been her student would have done wonders for me.” (as subject of sentence)
2. “It’s a nice thought
to have been her student.” (as complement)
3. “The ultra-savvy investment advisor was found
to have been a fraud all along.” (as adverbial modifier)
Usage 2. As noun form to denote a state or action in the past that is no longer subsisting (used with the passive form of such telling verbs as “say,” “believe,” “consider,” “assume,” “suppose,” and “think”):
1. “She is reputed
to have been a great beauty in the 1960s.”
2. “Houdini is believed
to have been the greatest escape artist of all time.”
USAGE OF THE PERFECT GERUND “HAVING BEEN”:The perfect gerund “having been” denotes a state or condition that no longer subsists at the time of speaking, as in the following examples:
1. “
Having been a student journalist is a big advantage to mass communication majors.” (perfect gerund as subject of the sentence)
2. “The former long-reigning monarch hated
having been deposed.” (perfect gerund as direct object of the verb)
3. “Edna seldom talked about
having been a beauty queen.” (perfect gerund as object of the preposition “about”)