Après j'ai trouvé ça, ça date de 2012 mais bon :
"It works one way, but not the other. You can use the keys gained in Steam (Right click on game in left-hand menu, View Game CD K*y) and activate them for your EA Games account by registering them at https://activate.ea.com, which makes them then appear in your Origin games list for installation. (This applies to most - but not all - EA Games that are available on Origin)
You cannot use Origin codes to apply games to Steam, and Steam won't let you buy DLC for games you don't own though Steam."
Qui dit en gros que Steam -> Origin ça a l'air de marcher, mais Origin -> Steam non