EDIT: How to obtain a Z visa?

Yes, you need the invitation letter. First, you should provide your passport and copy of its data page, the completed application form attached with 2 passport-style photos, the invitation letter of duly authorized unit, letter of undertaking from your company, tax certificate, copy of your company's business license, bank statement and the invitation letter from the Chinese business partner, as well as other required documents. Next, submit the application to the Chinese embassy.

Thanks for the reply. It seems that two letters are necessary. One from the business partner and the other from a government office in China. Does the business partner have to arrange that one too?

You can ask your business partner to arrange that one for you.