download This

and then:

-- What is this?--
This is CFW work on PSP2000.
This is the 6.37 ME-6 PERMANENT for slim psp's ONLY!

--How to Install--
First, you need to install CFW or HEN(ex. 5.00M33 , 6.20TN ) in your PSP.

1. Place the EBOOT.PBP from the .rar into ms0:/PSP/GAME/UPDATE/EBOOT.PBP
2. Place 637.PBP official from the .rar into ms0:/PSP/GAME/UPDATE/637.PBP .
3. Run installer from xmb.
4. gongratulations, you now have 6.37 ME-6 installed permanently.

this is what i used to upgrade from 5.00 m33-6 to 6.37 directly.

one thing to note is that when you run the installer, press and hold down left trigger + triangle to disable the installer's battery check.
if you don't  do this, no matter how full battery you have, it will say you need a full battery and exits.