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You can capture that Ghost pokemon if you lose the the elite 4 exactly 300 times and then talk to your mother when the game restarts on the 300th time. Your mother will tell you that she is sorry one of your Pokemon died in the last battle. The first Pokemon in your party will no longer be there, but it has to be a final stage Pokemon at level 100 for this to work, otherwise ghost won't appear! Then you go to the cave where you find Mewtwo and your Pokemon will be there. It will be a ghost, but you have to fight it. You can't capture it, you have to kill it. It will be level 200 and know all the moves in the game and be really tough, so be sure to prepare for it.
When you defeat it, it'll say that its spirit still wonders. You have to go to Lavender town ghost tower and find it in the wild. You'll know because it'll be Ghost instead of Ghastly, but it will have the name of your Pokemon. You can capture it with anything. When you have it, it stays as Ghost. It only knows the move "Friday 13" which makes the other Pokemon too scared to move. When it reaches 0 PP it steals the soul of the other Pokemon.
all of this has to be done without the battery dying. If you turn off the game or the battery dies, you have to beat the Elite 4 300 times again.
