How to check which employers actually sponsor H-1B
A posting that says it will sponsor is not a filing record. Check the USCIS employer data, the Labor Department filings, the debarment list and the posting itself, in that order.
sponsorship
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What no sponsorship in a job post means, and what it does not
A job post that says no sponsorship usually means no H-1B petition. It does not by itself rule out OPT, CPT or STEM OPT. Here is what each route asks of the employer.