bballman -- Congrats to your son on his offer!
Generally speaking, I don't think you will gain any favor early on, by telling Head Coach "B" that you have another offer to consider OR, any details about it. If Coach "A" sees enough potential in your son to offer legitimately and early, you can be sure he will expect him to be offered by other schools and conferences. Don't use that offer to "put him in a corner" as it could back fire. Remember, he too has other options that he will quickly move on to.
I believe that we know each other and I'm pretty sure I know who your son is and where he's played H.S. ball. I wish him all the best in this. The D2 Schools and conference that I think you are entertaining offers from; is top notch. There are some high character coaches and well respected staffs among them. PM me and perhaps I can share more detailed info about the schools you are considering, based upon our experiences.
Our experience was that the Coaching Staffs that offered early, with strong offers, had the best records, had programs with great reputations and proved to be the most open with us from the get go. They made a fair offer and wanted, in return, a well thought out answer in a respectable amount of time. They want to tie players up before the bewitching "signing" hour.
Probably the difference in our approach, was that we had done our homework, knew about the various coaches programs and their reps, and knew a good offer when we saw it. That coupled with it being a program and school he wanted, made that commitment an easy one.
Many offers, even D1, came later but none, in retrospect, were any where nears as valid as the one we felt strongest about.