Can my wife apply for the S1 if she is already in China, or does she have to go home first?

We've been living in thre for 3 years, her student X type is about to run out, but my course and visa has two years to go. Instead of signing her up for another Chinese course, we'd like to apply for the S1 type. Can we do this in China, or does she have to apply to the embassy in our home country? Also, we have our original marriage certificate from our home country, do we need to get this notified before applying, if so where?