After you help introduce Yugiri to Limsa Lominsa's secret fraternity to learn their fighting techniques, she asks you to convey her thanks to Minfilia.
This quest is available if you have completed the quest When Yugiri Met the Fraternity.
Starting the Quest
Talk to Yugiri south of the Aetheryte Plaza in the Limsa Lominsa Lower Decks to begin the quest.
Speak with Minfilia
Go to Revenant's Toll in Mor Dhona and go into the building south of the Mor Dhona Aetheryte to reach the Rising Stones. Enter the Solar and talk to Minfilia to complete the quest. There will be a cutscene.
Next Main Scenario Quest
After you complete the quest, talk to Minfilia to accept the next quest: The Great Divide.