On your old version, SAVE INSIDE OF the Olivine PokeCenter, then close the game.
Press F1 to continue
Replace your old .gbc file with the new .gbc file
* Don't forget to make sure your .gbc and .sav file are named the same thing!
After entering the overworld, walk down and exit the Olivine PokeCenter.
Once you're outside, press A on the "POKE" sign on the building.
* If the game needed to fix anything in your save, you'll be warped inside the building. Your save is now updated, so go ahead and save the game.
* Otherwise if you hear a "ding" sound, everything's fine and you can continue your adventure.