Instructions
Open a Web browser on your computer, and go to the download page for Custom Firmware 5.50 Prometheus v4 (see Resources). Save the file to your desktop.
Double-click the ̶0;128145_550_Prometheus.rar̶1; file to view its contents. Extract the 5.50_Prometheus folder by dragging it onto the desktop.
Connect your PSP to your computer with the USB connector cable for your PSP. Click on the Windows ̶0;Start̶1; button and select ̶0;Computer.̶1; Locate the PSP icon under Devices with Removable Storage.
Double-click the icon to display the contents of the PSP. Navigate to the ̶0;PSP̶1; folder and then go into the ̶0;Game̶1; folder.
Drag the 5.50_Prometheus folder from the desktop into the ̶0;Game̶1; folder for the PSP. Disconnect the PSP from the computer. Navigate to the menu on your PSP, and run the installer for 5.50 Prometheus v4.
Restart the PSP to boot the machine with the firmware update.