Talk to Doryani at the Origin Tower

In the 'Legacy of the Precursors' quest, I was heading towards The Patriarch Halls for the fragment. After defeating the boss, I invited my friends to my party. The quest item dropped only for them, but it didn't drop for me. Now, my quest to 'Talk to Doryani at the Origin Tower' is bugged because I don't have the quest item.
https://imgur.com/a/b9YRZj6