There is a program called Rein (old name: Rain) which allows you to copy your saves from an original DS game to a compatible GBA media adapter. I havn't used it for a while, so I cannot remember the specifics of how to use it, or what any newer versions are like.
Yeah, I'm using Rein but it seems to fail me when trying to extract save files from my Jump Superstars and Mario Kart carts.
Which Rein are you using? There's a version of Moonshell with Rein built into it if you want to try using that one. It's available on Infantile Paralysiser's site.