"Putlibai very fondly used to call Putlibai's son, Moniya."
The Pronoun 'Her' should replace 'Putlibai's' in the above sentence.
As per the list given to me 'her' is a Personal Pronoun. But here I feel 'her' is a Possessive Pronoun. What is your take on this?
I will be grateful if you can help me with this also.
Of course "her" is a personal pronoun! Possessive pronouns are just a sub-class of personal pronouns, that's all.
The system of person clearly applies to the possessives: "my", "your" (sing), "his"/"her"/"its", "our", "your" (plural) and "their" are all possessive pronouns of the 'dependent' kind, i.e. those that usually function as determiner to a following noun: "My key" / "Your house" / "Her car" and so on.