If you want a genuine FAA CPL that you can use (as opposed to just showing them your current licence and getting the FAA equivelent, which generally only entitles you to PPL privilges) then you need to do:
FAA medical
FAA CPL written
FAA CPL flight test
There are also specific breakdown for type of hours.
And if you want IR privileges I think you might need to do the FAA IR as well (written and flight test).
If you call 0500 895048 evenings, then they should know the answer.