Father-in-law is a USA citizen currently in China on a Q2 type.

If you want to change the Q2 into a Q1 type in mainland China, first, prepare the required documents include his passport, the application form, a passport-style photo, valid registration form of temporary residence, an invitation letter from the inviter and copy of the inviter's Chinese ID card, as well as your relation certificate, and other documents the consular officers consider necessary. Then, submit the application to the local PSB to apply for the extension. The Q1 type usually has single entry, after getting the Q1 type, then your father-in-law can get a Chinese residence permit which allows him to exit and enter for multiple times within its validity.