Applying for a Z and an S visa together

Hello,
I am from India and I will be applying for a Z type once I receive the required documents from my employer based in China. I have a question regarding applying for an S type for my wife. I checked the requirements above and I see one of the requirement as "4. A photocopy of the inviting individual's passport and residence permit". Now as far as I understand, I will get the work permit and an invitation letter from my employer right now. I will then have to go to China and convert my Z type into a residence permit. Does that mean I cannot apply for an S type for my wife now with my Z type? Do I have to send a copy of the residence permit once I am in China to my wife here in India and ask her to apply for her S type? That means we can't travel together to China. Kindly help me out if I am missing anything here.

Thanks in advance,
Pratik