In 1998 I entered USA and POE stamped B-2, later I found that it should be B-1 so I can get paid, and University filed petition to convert B-2 to B-1. They told it should take 3 months, I had to leave in 2 months but they told it is ok, as soon it will be filed....
I do not know if it is possible to convert to H-1. I did convert to H-1 during my next visit which was J-1 entering.