It should. It's common for people in North America to remove the KP-39 turbo and replace it with a GT1749VB.
The exhaust pipe just bolts right up exactly the same.
One thing that's different is the EGR pipe that goes from the exhaust manifold to the EGR cooler. It may be completely different on European cars though, as I see you are in Denmark. On the North American cars you need a longer pipe, which is readily available here from most TDI part vendors.