Most likely, you will train starting in Dec and not finish until Jan if your conversion date is not the same month as your training date. I believe your pay will begin at the new rate in your conversion month. Most likely that means that you will finish your last bit of sims and start OE on A pay but will do some of your sims under B pay (and probably fly half a month as a B on your old plane before sims start).

Please correct me if I am wrong, but I think that is what my A sim partner told me when I was in sims as a B last time.