It is not quite that easy. First, if he came here under a student visa, he must apply for a change of status from F-1 to H-1B. He would have to find a company that would sponsor him, which is not that easy given the various requirements and the limited number of H-1B visas available annually, i.e., 65,000.
USCIS is closely scrutinizing applications lately to ensure that the sponsoring companies are indeed who they say they are and not a way to bring in immigrants who have no intention of returning home. There has been extensive fraud, especially among Indians, to set up these phony companies to bring in people for a profit. And once you stop working for a company, you must find another sponsor, or else you must go home. The total H1B visa time is six years. A company can sponsor you for permanent immigrant status. If not, you must go home for at least a year, then apply again.
There are plenty of other rules and regulations that can impact someone trying to change an F-1 to an H-1B, but suffice it to say, given Sarkar's educational pedigree, he could parlay that into an H-1B.
I would like to see a chronology of his immigration status from the time he arrived here until now. I venture to say that there is a reasonable possibility that he is in violation of his immigration status.
40% of the 12 to 20 million illegal aliens came here legally and overstayed their visas. It is also instructive to know that 60% of all green cards are issued to people already here thru a change of status. Once you get here, it is very difficult to deport you, especially under Obama who has virtually stopped enforcing our immigration laws.
I believe we agree on everything except one point.
Currently, about 200,000 foreign STEM graduates are working full time in the USA under various kinds of non-H1B visas: student, internship, training, travel, etc.
You seem to imply that foreign STEMs cannot apply for Green Cards unless they have a H1B visa. I believe that is incorrect, but I don't have a link that confirms my belief.
I do know one thing for certain via a Center for Immigration Studies researcher:
80% of Chinese, Indian, Russian, and Eastern European STEM PhDs are still working in the USA five years after they received their degrees.