Total_Noob is very busy these days, But on the PSPKing.de forums he has commented on a 6.20 TN-B (HEN) release that will support the PSP-3000 4G models. Currently people with the newer PSP-3000 4G model’s have to try the unofficial 6.20 TN-A (HEN) patch by Vflame. Even with this patch users are still experiencing problems running homebrew and crashes.
6.20 TN-B will solve this issue.
Quoting Total_Noob:
Das ist weil du eine 4g model hast. TN-B wird 4g unterstützen
This is because you have a 4G model. TN-B will support 4g