American citizen living in Beijing with American spouse who is a student

Hello,

I am an American citizen already in Beijing on a tourist L. My husband is also an American citizen here as a student at Tsinghua and was issued his student X 2 weeks ago. Now that the October holidays are over I would like to change my tourist L type to spouse of student X. What is the process for people who are already in the country? Also, our marriage certificate is back in the US but my mother-in-law has sent us a scanned copy of it. Is that acceptable?

Thank you.