Walkthrough
After defeating the Elite Four, you can find Archer, the former Admin of the now disbanded Team Rocket, at the bottom of the Rocket Hideout in Celadon City. He will be in the room that once belonged to Giovanni, and he'll question why you are there before challenging you to one last battle. After defeating Archer, he will read you the letter he actually wrote you. He will say that he holds no grudges against your trainer, but he will make mention of him leaving the Kanto Region in order to build an even stronger Team Rocket. Archer will tear the letter before leaving.
Pokemon Trainer Archer
Level 54 Electrode: Thunder, Foul Play, Explosion, Reflect
Level 54 Golbat: Air Slash, Crunch, Sludge Bomb, U-turn
Level 54 Magmar: Fire Punch, Thunder Punch, Clear Smog, Brick Break
Level 54 Weezing: Dark Pulse, Flamethrower, Sludge Bomb, Shadow Ball