Additional Info
Yes, I did go to SS Office. Actually, I am in NJ and went to Newark INS building. SS Office is next door to the place where you get GC stamped. I filled out a simple form they provided me in the office. I do not remember what. I think it is the same form which is used for change of address etc. The whole process took about 10 minutes. I do not think we need to get our license updated as it does not have any immigration related information.