Converting 9.9 to a 15 hp

[96Johnson9.9]

I have a 1996 Johnson 9.9 (Model J10RELEDD) that needs the carburetor rebuilt, but I am considering installing a new 15hp carb instead. From what I have been told by others, and from everything I can read online, replacing the 9.9 carb with a 15 carb will is all that is required to convert my motor to a 15hp. The problem is I can't tell which carburetor from the parts site is the one I need. The 15 HP carb is supposed to have a larger throat and main jet, but all of the carburetors on this site are listed for both the 9.9 and the 15 models. Does anyone know which carburetor I should purchase?

[boats.net]

Never tried it, we don't alter horsepower on engines so not sure which one would work.