Thats simple. First, go to [Guide] Unbrick or Downgrade any PSP using the Pandora Battery - QJ.NET Forums and follow the guide on Memory Stick Preparations.
Once you got your magic memstick, work on this [GUIDE] Unbrick a PSP Slim or Classic. - QJ.NET Forums in the Getting Ready section starting from the 4th bulleting.
Once your done, you should have a Despertar Cementerio, a universal unbricker/upgrader for fat or slim to 3.71 M33. On how to use it, read the second site i gave.
HOWEVER, you can't do any of those if you dont have a cfw psp at the first place. Since you "can't just have a complete copy of the directories of magic memstick". There is a need to perform IPL partition and obtaining "msipl.bin" specifically to make a magic memstick.