A Rising Star

 is a task in.

Synopsis
Bekarna might have regained her mind, but she still needs her grimoire returned. Problem is, it was lost somewhere in the Archives section of the facility.

Walkthrough

 * Bekarna's grimoire is located in the Quarantined Section, in the southwestern room. The other part needed is in the Restricted Section, in the Catalog Room (you're looking for Catalog Record: Bekarna's Celestial Grimoire). Collect the two, then return the completed Celestial Grimoire to her. She will ask for a piece of starmetal next, triggering the final piece of her questline.