So here is a quick Guide to doing so.
There are two guides so read carefully.
Guide 2
This is the easy way to install 1.50 homebrew but only works if there is an eboot in the /PSP/GAME folder.
Put your 1.50 homebrew in the folder
/PSP/GAME150
Either put your 3.03 homebrew in the folder or Create a folder named "__SCE__"
/PSP/GAME
Guide 2
Quickly power off your PSP
So that your PSP completly reboots. It will show the "Sony Entertainment" logo.
Quickly hold down the RTrigger.Note if you are having problems completly turning of your PSP unplug the PSP and remove the battery.
This will bring up the built in recovery console in 3.0x oe
Select Configuration and press (X)
This will bring you to a submenu. It will allow you to adjust your 3.0xOE to suit your own needs.
Click on Game folder homebrewBack
Skip SCE logo (currently: enabled/disabled)
Hide corrupt icons (currently: enabled/disabled)
Game folder homebrew (currently: 3.03 Kernel)
Autorun program at /PSP/Game/BOOT/EBOOT.PBP
Use NO-UMD (currently: enabled/disabled)
Fake region (currently: enabled/disabled)
Free UMD region (currently: enabled/disabled)
Note: If its already on 1.50 Kernel then there SOMETHING WRONG