Internship Shanghai

I am doing an internship for a swedish company in Shanghai, for 11 weeks this fall. Chinese visa application center say that i need a working Z type. The company say that it costs too much and is too hard to get. Can i get by on a F-type? I asked the companys travel-specialist that said a f-type is only valid for 30 days, sometimes 60.
So thankful for your help!
Forgot to say, the internship is unpaid.