To use this downgrader, you will need the following:
A legal Lumines UMD, either the EU (ULES00043) or US (ULUS10002) jap (ULJS00005) the original Lumines and (ULJS19005) The Best version. The original, Platinum, or Greatest Hits versions are all fine.
If you have 3.10-3.11 or 3.30-3.40 upgrade first to 3.50 !
download 3.50 firmware:
Unzip and copy the file into PSP/GAME/UPDATE (make a new folder UPDATE inside the game folder)On the PSP, run the 3.50 update from the memory stick under the Game menu.
Delete PSP/GAME/UPDATE or format your memorystick after the update!!!!.
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Downgrade
Download: 3.50 Firmware Downgrader :
PSP Firmware Update 1.50:
you can follow the steps below or use 3.50 easy downgrade and skip to step 4! 3.50 easy downgrade:
Extract the folder to your desktop and copy the psp folder to your memorystick.
Instructions:
Important : Format your memorystick before and after each upgrade or downgrade !!!!! Your battery should be fully charged, or close to full. You should also have the PSP plugged in with the charger. Do not disconnect the charger, remove the battery, remove the memory stick, or press any buttons while updating. NOTE:
Before you start ! psp language must be in english!!
Change the language to English, under System Settings -> System Language
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step1: Extract the 3.50 downgrader (use winrar) to your desktop.
step2: open the 3.50 downgrader folder and copy the psp folder to your memorystick.
step3: Extract the PSP Firmware Update 1.50 file to your desktop and Rename the EBOOT.PBP to UPDATE.PBP and copy it to your memorystick : PSP/GAME/UPDATE folder .
step4: Load Lumines and press x to start the game, The screen will clear to black and fill with a light blue colour, then the PSP will reset itself.
NOTE: When you run the program, you'll see a coloured screen that can be one of two colors:

* Red: the files couldn't be written to the flash (it happens a few times). Just keep trying.

* Pale Blue: The files were written succesfully, and HEN is active. After that, the xmb will be rebooted.
Note that a pale blue screen will appear again every time the PSP reboots with HEN active.
step5: Check that HEN is running by going to system settings, then to "System Information" and it should show up as system version 350 HEN
step6: If it is showing up as system version 350 HEN then Now go to game/memorystick and run the downgrader , which will show in the xmb as "psp Update version X.YZ"
Once you have agreed to start the downgrade do not unplug the
PSP, or try and restart it. you will see the progress don`t touch anything!! till it finished!!
step7: Once finished the PSP will show a big OK and ask you to press X, and restart itself.

congratulations you have a 1.5 psp !
(If it comes up saying that the settings are corrupt, press to continue, this will mean you will need to re-enter the settings for network connections into your PSP.)
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Extra: if you wanna upgrade from firmware 1.50 to the custom firmware 3.40oe-a of Dark Alex.
Download this easy upgrade

click on the icon
Extract the file (use winrar).
put 340oeflasher and 340oeflasher% folders into the psp/game/ folder on you memorystick.