Yes you will need an amendment and your wages will need to be equal to or in excess of the prevailing wage for that state. It is up to the employer whether to allow you to work remotely and establish guidelines so it is clear you are working under their control and direction; otherwise your employment will not be H-1B eligible.
Lynne R. Feldman, Attorney at Law
Concentrating in Immigration and Nationality Law
2221 Camino Del Rio South, Suite 201
San Diego, CA 92108
phone: (619) 299-9600, facsimile: (619) 923-3277
Formerly Adjunct Professor -- Immigration law
University of Illinois College of Law
Your employer needs to retain an experienced immigration lawyer, whether myself or one of my colleagues, to review all the facts, advise them, and handle the case.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.