If you fight and beat the elite four and the champion he will reappear, the same as all other legendaries in HG & SS.
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You restart the game.
you go back to the cave where you caught groudon/kyorge
you cant but you can trade it from Pokemon soul silver
No you can only get groudon in Pokemon ruby or emerald and transfer through Pal Park or if you have heart gold or silver soul you can catch and trade groudon to yourself
you go to professor oak and he will say to get kyogre and kyogre will only appear with a silver soul and a golden heart which means that you will have to trade from heart gold