The Umbra Map is said to be part of Morgal's oldest records (It is not explained how it got there, given that Morgal was only recently founded). Following Sana's annexation of Morgal, the Umbra Map as well as other treasures, were taken by the Sanans as spoils of the war. It would fall into the hands of Lord Kuan, who would later die in the Morgal Revolution.
Matthew's travels to stop the Grave Eclipse leads them to Himi, who has a prophecy which reveals the map's existence and it's orignal location. Sveta, a member of Morgal's royal family, reveals the map's current owners are the Sanans. The group travels to Tonfon, and speaks to Emperor Unan, who notes that the only person who could have the map is Lord Kuan's son Ryu Kou, whom Matthew had met earlier.
Matthew uses Lady Hinechou's Echo Gem to track Ryu Kou down to Iceberg Outpost. During Hou Zan's funeral, Kraden will ask Ryu Kou if he has the map. Although reluctant, he will hand it over. After acquiring the map, the group realizes that finding the locations of the gear will not be as simply as they thought, since the Umbra Map is ancient and Weyard's geography has changed since then. After a bit of study, Karis will mark the locations of the Umbra Gear on the player's world map.
The locations of the Umbra Gear are: