Tourist L - Upgrade to Student X

Hello!
I want to study in Beijing for 6 months. I already received th "Visa Application for Study in China" (JW202). Unfortunately, I lost my passport. Now, the Passport No. written on the "JW202" sheet and the passport no. are different.
To make a long story short, I wanted to ask, if it's possible to go to China with a tourist Visa, and then extend it in China to a student (F)? And how much would it cost? Would I have to make a Visa-run to Hongkong?

Regards,
Frank