I haven't bought a new P-32 since the lettered prefix system went into effect, so I'm not sure how they're lettered... apparently the H is used for the P-3AT (at first, at least).
So, all I could say right now is that you've got one of the newest P-32s.
Any P-32 over the serial #9600 range has all 'updates', anyhow... so no problems in that regard.
My guess is Bloodwalker will come along in due course and enlighten us on the process.
Flyer