Mognet Central is a side quest that involves delivering mail from one Moogle to the next as you progress through the game. Each Moogle that you visit could potentially give Zidane a letter when the “Mognet” option is selected as well as a Kupo Nut (check out the Kupo Nut side quest page for more information). Be sure to select it each time you meet a new Moogle.
Some of the deliveries can be missed entirely, so be careful to always check Mognet when given the opportunity. Many of the letters delivered are from one Moogle to the next Moogle that you will meet, but you can complete the section below regardless of how many letters you previously delivered.
Once you have reached Disc 4 you can complete the Mognet Central side quest. Speak to Kupo in Alexandria (who can be found in the Steeple next to Stiltzkin) and obtain the letter for Alta.
Travel to Burmecia and find Alta all the way in the back. He will give you a letter for Mogryo.
Mogryo can be found in the Black Mage Village near the Chocobo hut. He will give you a letter for Kumool.
Kumool can be found inside Ipsen’s Castle in the second room. He will give you a letter for Mois.
Mois can be found at the entrance to Fossil Roo which can be found in Qu’s Marsh on the Mist Continent (the one near Lindblum). You need to have Quina in your party. Mois will give you a letter for Noggy.
Noggy can be found on the upper level of Daguerreo. He will provide you with the final letter for Kupo back at Alexandria in the Steeple.
The final letter mentions that someone in Alexandria has something called a Superslick. That person is Ruby down in the Mini-Theater. Speak to her and she will tell you that she has it hidden in her hair.
Obtaining the Superslick from Ruby in Alexandria is the requirement for obtaining the Well Lubricated Trophy.
You now need to jump on your Chocobo which should have the Ocean Ability (from completing the Chocobo Hot & Cold side quest and the Chocograph side quest).
Travel to the island north of the Outer Continent shown in the map and screenshot below. Use a Dead Pepper to break open the crack in the mountain and head into Mognet Central.
There is a short scene that occurs when you speak to Artemecion on the second floor at the end of which you will receive a Protect Ring as the reward for completing this side quest.
Repairing the machine in Mognet Central using the Superslick will net you the Back Online Trophy.