回复：You should be fine.

So you think i should be fine with a copy of I797B H1B notice (not original) and of course the copy of original support document for H1B prepared by attorney with me for new I94 in the case I surrender my multiple H1B I94.

I am thinking to just keep the multiple I94 cards anyway while leaving, could this cause unnecessary problem when coming back. at least when under TN, I was travelling between US and Canada via air, I do not need surrender them, just keep use it if still valid.

Could it be different for travelling to China or other country though?

Thanks for replying.