Frequently Asked Questions - SB-1 Visa
A Returning Resident Permit, or SB-1 Visa, is what a Legal Permanent Resident (LPR or Green Card holder) can get to return to the United States after being out of the country for more than one year. When an LPR leaves the United States, they must return within a year. If they stay more than a year, they must obtain a Returning Resident Permit in order to return. This also applies to those who remain outside of the country longer than is allowed by their reentry permit.
You apply for a returning residence visa through the consulate in your home country. There, you have to explain in quite some detail the genuine reason for your inability to return to USA within one year. It is discretionary upon the consulate whether they are convinced by the genuineness of your response or not.
For more information, see this State Department’s webpage: http://travel.state.gov/visa/immigrants/info/info_1333.html
About Returning Resident Visas (SB-1)
1. There is no such requirement that I am aware of at this point today (June 2017) that you have to notify any US government agency or Indian government just because you received your Green Card. However, what you should do is you should inform your employer that you have got your Green Card so they can update your Form I-9 which is an internal matter within the files of the employer. They don't have to update any government agencies.