Since the locationofyoyr job has changed, your employer needs to refile an H-1B petition
Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
Your employer will need to submit an amended H-1B petition noting the location change. As far as the green card is concerned, green card process is very lengthy and will not provide a quick solution. You still need to amend H-1B.
1) Employer will seek to amend the current petition
2) Green card (immigrant visa) process is independent of H-1B (non immigrant work visa.) Depending on the category and country of charge ability, an immigration attorney can guide your employer after a careful review of the pursing the job requirements and your qualifications.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. You are encouraged to seek independent and private counseling for a complete review of your case.