you just arrived in Beijing on a tourist visa, and you want to do convert your tourist visa to F visa so that you can do your internship. I think what you need to do is to do the temporary residence registration at local police station, instead of the residence permit( residence permit is a visa type which is granted to foreigner employees or students). The interrelated units should make the registration if the foreigners stay at hostel, hotel, school dormitry etc. And you need to register at local police station if you stay at an apartment.
You can first register at your friend's apartment and have the police registration of temporary residence, then you can change your L visa to F visa. After you have your own apartment, then go to the local police station to register again on a F visa you got in Beijing.