Not sure on compatibility, but regardless, the tuning is archaic and i would NOT advise running it on your 06. Get a cheap SCT 3015 tuner and some custom tunes from a vendor of your choice. You and your truck will be happier that way.
Definitely go with SCT and get custom tunes. Back in the day, h&s did not have trans tuning for the 6.0 (don't know if it is still the same today). Also, sct custom tunes will be safer and more powerful.