Please +rep if I helped you
This firmware is signed which means that you do not need to load HBL (Half Byte Loader) All you need to do is
1. Download the Link provided below and unrar
2. Connect PSP to computer via Usb cable
3. Copy TN_HEN to "X:/PSP/GAME/"
4. Disconnect usb from psp
5. Load TN_HEN from game and wait for 10 seconds. There should be a black screen. After you will be lead back to the VSH menu. Check your System Software in the settings. It should say "Version 6.20 TN-E". Congrats you are now on 6.20 TN-E.
6. Run that and always use that when you need to go back into 6.20 TN-E.
Download: 6.20 TN-E