回複：F-1 => J-1 => Others?

You have to register to the Education section of Chinese Consulate in your region first. If you had done that after you arrived at USA, that is OK. You don't have to wait one year for your waiver. You can do registration and waiver together only if you pay the money and fill a registration form.( check the website of Chinese Embassy). Ask you boss to write a letter to the Chinese consulate to say that he will apply H1 visa for you after your j1 visa expire.