If you are saying that the company you are working for is going to sponsor H-1 visa for you, I assume that you are on some other visa or maybe an OPT? Now like Faith777 said, if your H1 is approved first, then the F1 I-20 would be in effect once that comes through and you would can't work full time unless you are on full time CPT or OPT. On the other hand, I believe that if your H-1 is approved second, your status would change to H-1 and you would be able to work, but may not be able to do your PhD full time unless you have enough time (you can still study full time on H-1, as long as you also work full time which is what the H1 visa is granted for).
