You have found F'lhaminn, and she is now ready to meet with Minfilia.
This quest is available if you have completed the quest Moving On.
Starting the Quest
Talk to F'lhaminn to start the quest. You will automatically go to the Waking Sands.
Report to Minfilia
Prior to speaking to Minfilia, you may wish to watch the videos listed on the "Moving On" quest page for more background information. Go east into 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: Laying the Foundation. There will be a cutscene.