How to play the Steam version of Battlefield 3 when you already have it on the E

Hello.

I have Battlefield 3 on my EA account, purchased via Origin/EA App a few years ago.

I had forgotten that I had this game on my EA account, so I ended up purchasing it again through Steam.

If I install and try to play Battlefield 3 on Steam, the following error appears in BattleLog: You need to install or patch the game before playing.

Now if I install and try to play Battlefield 3 directly through the EA App, it runs correctly.

The question is: since I already had this game on the EA App and now I bought it on Steam, will I not be able to play it on Steam? Is there any way to work around it so that I can play the Steam version and not the EA App version?

I use the same email on both Steam and my EA account.