Instructions
Return to the home screen on your PSP and select the ̶0;Settings̶1; option from the main menu.
Choose the ̶0;Network Settings̶1; category from the Settings menu and then select ̶0;Network Update.̶1;
Click the ̶0;Download (receive data)̶1; button in the menu and select the ̶0;Update (software update)̶1; option. Your PSP 1001 will now be updated from 5.03 to 6.20.