transfer a game from EA to steam

Hello,

I bought Plants vs Zombies GW2 about a year ago.

I now would like to transfer the game on my steam account because I find it more convenient to use only one platform to access the game. But the code of the game doesn't work and I can't find a way to resolve this.

I also couldn't find a way to link my two accounts from steam though I did it from the EA platform.

Thank you for your help