It's been a while since I last replayed it, but I think there's an option on the main screen that shows extra postgame missions and that doesn't go away even if you reset the game? Called Ranger Net or something.

If it's there, you'll be able to look in it and see if the Manaphy Egg mission has been done already. It's called "Recover the Precious Egg!" and if it has been done, when you select it you'll either see a cutscene of a woman singing to the egg (in which case it hasn't been transferred to a Sinnoh game and that can be done) or someone talking about how they hope the egg is doing well (in which case you won't be able to get the egg).

If it's been taken, you'll have to use external devices to reset the cart. It won't respond to the regular factory reset button input.