With a PSP, in order to update the firmware, you have to follow a couple of steps.
However, they are fairly simple steps that don’t require much technical know-how.
On the stick, create a folder called PSP, then create a folder inside that called GAME, and finally create a folder inside GAME called UPDATE.
You can update the system software for the PSP™ system using any of the methods listed below.
You need to have a wireless internet connection in order to use this method, so if you connect your computer via a cable or telephone connection and don't use the internet on your PSP, you'll need to choose a different option.
If an update is cancelled before completion, the system software may become damaged and the system may require servicing or exchange. When connected to the network, the system scans for the latest update data.
Follow the update instructions and let it do its thing.
source Place the update file "EBOOT.pbp", inside the following folder on your PSP: PSP/GAME/UPDATE/If it's a PSP Go, place it in the system memory, not on the memory stick.
In order to update PSP firmware with the network, a wireless internet connection is required.
The firmware update occurs automatically and it is the easiest way to upgrade the PSP.