Quest on Transmutter

In, Green Despair (GD) look for Port Manager Karter. He is beside the Armor NPC.

Then go find Yerte(Core Alchemist) in Port Lux. Just Straight and the last NPC on the left is Yerte.

Then talk to him you will find there's quest about transmutter. Then, after you get the quest you need to talk to all the Core Alchemist in town (Green Despair,Dessert Scream,Bloody Ice).
After you finish all the talking you need to go back to yerte.Then, yerte will ask you to choice what kind of transmutter you want, choose what you want and there you have it your transmutter.