Here is a guide for downgrading any current PSP hardware version TA-079 - TA-086) from firmware 2.81-3.03 to 1.50.
If you have a 3.03 PSP skip to step 4
1) Download 3.03 update from link above. Unzip and place the file in :/PSP/GAME/UPDATE
2) On the PSP, run the 3.03 update from the memory stick under the Game menu.
3) Delete :/PSP/GAME/UPDATE
4)Copy the contents of the folder MS_ROOT from the 3.03 downgrader package to the memory stick
5)Unzip the 1.50 update to a temporary folder. Rename the EBOOT.PBP to UPDATE.PBP and copy it to :/PSP/GAME/UPDATE/ .
DO NOT OVERWRITE PSP/GAME/UPDATE/EBOOT.PBP!
6)Load GTA LCS. It should get to loading savegame, then the screen will clear to black and fill with a light blue colour, then the PSP will reset itself (if this does not happen see section below)
7) Check that HEN is running by going to system settings, then to "System Information" and it should show up as system version 303 HEN11 - If it is showing up as HEN then go to the memory stick and run the x.yz update
8) If you have an unpatched TA-082 or higher motherboard, you will be prompted to allow the downgrader to patch your motherboard so it can be safely downgraded. The downgrader will not let you proceed without patching, if your motherboard requires it.
9) Before the downgrader does anything to your PSP it will ask for you to agree to what it is doing, if you no longer want to continue press the Right Shoulder Button (R-TRIGGER).
10) Once you have agreed to start the downgrade do not unplug the PSP, or try and restart it
11) Once finished the PSP will ask you to press X, and reset itself
12) If it comes up saying that the settings are corrupt, press x to continue, this will mean you will need to re-enter the
settings for network connections into your PSP, otherwise go to step 14
13) Load the included NetConfigBackup application in your PSP, and select to restore, this will take the backup that was done of the network config that was done automatically during the downgrade.
14) All done now. Hopefully you now have a 1.50 PSP.