I've seen multiple H-1B's get promoted to management. It totally illegal and should be reported. Yea, I'm talking to YOU! Here is the statute. NOTE: That you have to come here as an execute, NOT BE PROMOTED.
EB-1C Eligibility for H-1B
According the the USCIS, the EB-1C is a green card with very specific requirements.
The petitioner must be a U.S. employer who has been conducting business at a foreign entity in a foreign country for at least one consecutive year.
You must have worked for this employer abroad for at least one consecutive year in the 3 years prior to filing your petition.
You must be coming to the U.S. to work as a manager or executive for that employer.