I'll just pop in to attach and post a quick comment:
MemcardRex (also attached) is a slightly more user-friendly program that can do the same thing on the computer side. You'll still have to follow the same procedure to get the file to your computer, but MemcardRex can handle more file types, including raws. I haven't used it myself, so I can't give a procedure on that.
PSXGameEdit (psxge160.zip) was taken from its author's site.
MemcardRex (MemcardRex 1.4.zip) was taken from its author's site.
PSX Raw Converter is the final file, psxrcv11.zip