You have learned all that is known in Little Ala Mhigo of the masked man, so you depart to report to Minfilia.
This quest is available if you have completed the quest Big Trouble in Little Ala Mhigo.
Starting the Quest
Talk to Gundobald in Little Ala Mhigo in Southern Thanalan to begin the quest.
Report to Minfilia
Use a Vesper Bay Aetheryte Ticket (which you received after completing the quest The Scions of the Seventh Dawn) to return to Vesper Bay. Go into the northwest building and enter the Waking Sands, then enter the Solar and talk to Minfilia. There will be a cutscene.
Next Main Scenario Quest
After you complete the quest, talk to Minfilia to accept the next quest: Terror at Fallgourd.