PSP firmware expects a specific encryption. While most saves work, some PPSSPP saves saved with "Encrypt Save" disabled may be rejected. In PPSSPP, go to Settings → System and check Encrypt Savedata before creating a save you intend to transfer.
Data miners found that MHP3rd’s save file contains a for your Felyne companions. If you never fed them before quests, the value dropped, affecting their AI (they’d gather less). The game never told you this. Only by hex-editing the save did players confirm it.
To properly handle your progress, you first need to know where the data is stored. On the PSP and most emulators, the file system is emulated in a specific way.
Navigate to your PPSSPP directory on your PC or mobile device. Open memstick -> PSP -> SAVEDATA . Copy the ULJM05800 folder. Connect your PSP to your PC via USB.