Instructions
Begin playing "Pokemon Sapphire" on one of the Game Boy Advanced systems.
Capture Latias on the "Sapphire" game. In order to have Latias available, you must have at least one Pokemon over level 80. Latias can be found in the Hoenn area. If not, fly around Mossdep City until Latias appears in the water. Land near where Latias appeared and search there. Be sure to have a lead party Pokemon who can use a sleep or knockout move as Latias will attempt to run away. Also, be very careful not to kill Latias (save after any encounter as her HP doesn't recover after running). Use a sleep/knockout move and capture Latias.
Save the game immediately after capturing Latias.
Begin the copy of "Pokemon Ruby" on the other GBA system.
Move your characters on both games to the upstairs of the Pokemon Center. Enter the middle door with both characters.
Trade the Latias from the "Sapphire" game to the "Ruby" game. The "Sapphire" game will no longer have Latias available.
Save the "Ruby" game.