Yes and it works like this: Your going to have to migrate your Pokemon from your gba Pokemon game to the ds Pokemon each Pokemon should hold an item that you want to give to the ds Pokemon game when you migrate those Pokemon play the ds Pokemon game to capture them in the pal park then go check the PC for the Pokemon you caught each should still be holding the item you gave them from the gba Pokemon game now all you need to do is take the items and now your ds Pokemon game has the items!
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If the game is fake you can't trade pokemon.
it is not possible to trade Pokemon with DS and GBA. you may if you have diamond, pearl, hg, ss, platinum you can MIGRATE Pokemon from GBA games to DS games. this can be done in the main menu under "Migrate From (name of your game)" example: Migrate From Firered or Leafgreen.
There is no way to trade between Emerald and Diamond, because they are for different systems. The closest thing is that if your friend has beaten the game then you can put your Emerald into his DS and put your Pokemon into his game. The only problem is that you can't trade Pokemon from Diamond to Emerald, only Emerald to Diamond. however there is a way to get the Pokemon from a GBA cartridge to the DS cartridge. when you get in to the Pal Park supposedly if you have a GBA cartridge in the slot2 and a DS Pokemon game in slot1 the Pokemon from the GBA cartridge will "migrate" to the slot1 game.
get a GBA to get it
I don't know anyone that has one {I wish I did}, but I know how to get one. Get the game Pokemon XD Gale of Darkness, catch Lugia, trade it on a GBA Pokemon game, and if you have Pokemon Pearl, Diamond, or Platinum, Migrate Lugia and 5 other Pokemon.