Here is what I am aware of.
Actions to take ASAP:
- Replace/update your SSN card. This can be done at your local social security center. See https://www.ssa.gov/
- If employed: ask the employer to update the I-9
- If you have some accounts at banks, insurance, mortgage: inform them about your residency status, as in some places you may be eligible for lower rate after getting the green card.
- If you are a male between ages 18 and 25 (inclusive, i.e. who have reached their 18th birthday and who have not passed their 26th birthday): register with the Selective Service (U.S. Armed Forces)
Things to do until you get US citizenship:
- Fill an form AR-11 (Alien's Change of Address Card: https://www.uscis.gov/ar-11) each time you move (AR-11 should be filled within ten days of moving)
- Carry proof of your permanent resident status at all times. (From https://citizenpath.com/carry-my-green-card-with-me/: "You are legally required to carry your green card with you if you are age 18 or older. Section 264(e) of the Immigration and Nationality Act (INA) states that all permanent residents must have “at all times” official evidence of permanent resident status. A photocopy is not acceptable. If found guilty of this misdemeanor, the penalty set by law is a fine of up to $100 and up to 30 days in jail.")
- Keep track of some information to be prepared to apply for naturalization in five years. Note that one can obtain the entries/exits to the US via a FOIA request.
- If you plan to remain outside of the U. S. for six months or longer, you are strongly suggested to obtain a 'Re-entry Permit" before leaving the U.S.
Also beware that your tax reporting will changes slightly.