Do R4 cards work with DSTT saves?

My DSTT card broke after a wonderful year of using it. I just ordered an R4 as that was the only one I could find from a reliable website. I read somewhere in a forum or something that the .sav files are formatted to the card they were made on. Is this true? I would really prefer not to have to start the games again as it would mean having to start some GBA games again too to get things from there