I am working in China. Can my wife apply for Residence Permit if she entered China using S2 Visa?

I have Work Z and currently working in Shanghai, China. I already have Work Permit and Residence Permit in China. My company offers me to work and move to another plant which is located on the other city in China. My wife already have S2 (in which she was granted 120days to stay in China). She also used my Shanghai documents for this S2 Application. Now, with me moving to different city, can she still use the S2 to enter different city? Then, if she passed the immigration and enter that city, can she apply for residence permit even though she entered using S2? Usually those with S1 Visa needs to apply Temporary Residence Permit before 30 days of their stay in Shanghai if they want to extend their visit in China.