Audi A4 1.8 Turbo 2003 computer change

Hello friends, this is a 2003 Audi A4 1.8 Turbo AWD. The original computer (8E0909518AF) burned out, and after about 10 minutes of warming up, it shuts down. I bought a used one with the same part number, but the transmission isn't working. I've done some research online and discovered that I need to adapt the new computer. The problem is that here in Honduras, VW, Audi, and BMW parts are extremely scarce, and I have no experience in how to do it. It seems easy, but I don't understand. I hope you can help me.