回複:This thing happened to my friend!
A few months ago my friend ted EAD application, and local officer asked him why he want to apply for it because his GC application was approved. Only at that moment, he knew that GC application was approved in March last year (more than one year). He didn't receive anything from USCIS (I am not sure if he registered on CIS website). From local office, he finally got his GC.
Anything can happen in GC application. About one month ago I received other's GC in my address (No address mistake).
Good luck!