You will find Rainn in the Balterossa pub. He's already traded it to someone else. You didn't think it would be that easy, did you?
Rainn tell you who he traded the treasure to, and will give you the Ancient Scabbard that he got for the treasure, but only in exchange for the Ring of Morning Calm he traded to Alyssa in Baaluk.
Alyssa is out on the streets of Baaluk close to the north exit of Grentze Commune. However, she is done with trading. Seems she got a fake treasure map from someone else in exchange for the Ring. She's willing to let you purchase the ring for 10,000g. You have the option not to pay, but she won't negotaitiate.
Back to Rainn at the Cafe Moondust in Balterossa. He then trades the Ancient Scabbard for the Ring of Morning Calm - you can decline first to get an additional Tuck. He tells you that Raphus' treasure is with Beauson in Elysion.
Now to look for Beauson in Elysion. He is under the bridge entering the Genaade District, in the lowest part of the area. He doesn't have anything to give you but information. It turns out the Beauson sold Alyssa the map she was so upset about. She thought it would lead to the treasure of the Imperator, but Beauson said that wasn't it at all. If you decline Beauson the first time he will accept the Royotian Wine instead of the Ancient Scabbard. If you decline a second time he will accept 10 Royotian Steel instead of either the Royotian Wine or the Ancient Scabbard.
Back to Baaluk, and speak to Alyssa. She tells you she threw the map away. Now you should be able to find the Map of Memories close to the entrance of the guild.
You may return to Beauson and accuse him being a fraud. He will give you the Irised Stone (special item, becomes a component after the quest) he took for the map to make up for it. Go back to Alyssa and show her the Stone she will say you may keep it and give you the Ring of Morning Calm again (this time it is an accessory).
Return to Raphus and claim your reward. He tells you that the map was something Raphus and his wife used on their adventures. It has a lot of sentimental value, but that's all. In return he rewards you with the an Irised Stone (component)
donc, tu vas à baaluk, et tu parles à la femme à droite du magazin d'éléments, de l'autre côté de l'entrée.