
Margaret, as she appears in-game.
A resident of the Velvet Room. She desires to know something...
Social Link : You can increase your Empress Social Link by spending time with this character.
Margaret has a younger sister named Elizabeth, who was a previous resident of the Velvet Room. She appears to help Igor also in Persona 3.
After entering the velvet room on the last day to save Kanji (June 4rth) an event began with Margaret alone in the room which then leads to a social link being made with her, whether this is do to the day of the visit or another requirement being met is unknown at this time as no amount of Google searching answered this question (that I found).
After looking at some of the information I did manage to find it may be possible that the event took place do to meeting the knowledge requirement to ask her request?