回複：然後自己把 I-797 訂到新護照上？還是總是帶兩本護照，直到重新續H-1?

You can use the new passport and the H1 approval notice to get a new H1 I-94 if you will leave US in the future. of course, if you go to Canada/Mexico again and will return within one month, you just do the same thing as you did last time (not provide the valid I-94, not get a new one).