HIB question.

Hi experts:

Puzzled with one problem.
I, right now, am working in an university, H1B visa. If I got a job offer. I can wait to next April to get a quota to transfer. Question is when I can start work. Next April, or Dec 1st? I know some one with same case, started work at this Augest. Where the H1B in unversity still make difference than those OPT and F cases.
Millions thanks.

Benben