You will need to use specialized software designed to install those games to your devices which you can backup right from your game discs or ISO's stored on your PC.
PS3 doesnt support Internal HDD for PS2 games. Open PS2 Loader (OPL) is an application designed to allow you to play your PS2 games from an Internal HDD, a connected USB device or a networked PC from either a PS2 console or a PS3 console that supports PS2 Backwards Compatibility. Open PS2 Loader Project v0.8 is released.
