File for a change of nonimmigrant status from H-4 to F-1. Of course, you have to be accepted to a program first. Speak to the DSO at the school for information.
If you have an employer willing to sponsor you and if you are otherwise eligible, you can file to change your nonimmigrant status from F-1 to H-1B.
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I agree with my colleague ... all the work will be done by the employer that wants to hire you.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.