I think a bit of detail is required. I haven't really kept up with hardware changes, but as far as I know the PSP does not read the same SD cards as most cameras, rather they only took the Memory Stick Pro Duo? I guess if there was an adapter for for the SD card to fit the Pro Duo slot it would work, but that's not something I would trust myself.

In any case, you can just copy the stuff from the old memory stick to the new memory stick. Just to be sure, you should probably format the new memory stick from inside the PSP (backup whatever's on there in case you want to keep it). Any saves will work just fine if you copy them over. I could send you my own saves for a game and it would probably work. It's pretty flexible that way.