I arrived here pon a J-1 visa and received a SS card with "valid for work only with DHS authorization" on it. Now that I have my GC I am assuming I need to apply for a new card with these conditions removed. Since I am of the understanding that my actual number remains the same, 1. do I need to apply for a new card? and can I continue working, using my GC as evidence of employability, whilst waiting for the new SS card?