Do not attempt to update directly from 3.10 to 3.90. Firmware 3.90 does not exist for retail PSP. The final official firmware is 6.61 (released 2015). Version numbers like 3.90 refer to custom firmware (CFW) versions (e.g., 3.90 M33, 3.90 GEN) from 2008–2009.
EBOOT.PBP for 6.61 → place in PSP/GAME/UPDATE/ → run from Game menu).Never use Pandora/Magic Memory Stick methods unless you have a pre-2008 brick to recover.