His immigration status doesn't matter, its the U.S. company that must sponsor you for the H-1B. Small companies sometimes struggle with evidencing the ability to pay the wage, but thats not always the case. If they are willing to pay the costs of the visa processing and attorney fees, its worth checking it out with an immigration attorney.
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Hopefully it is a corporation ,... that is a US citizen and can do the papers.
If it is such a small company that they haven't become a corporation ... then you should probably keep looking for work ... small companies have a hard time getting H visas.
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