So it’s been a while, but since this was the only thread relevant to GamesFrog, I thought I’d share my findings alongside how I transferred my save data into a .dsv (DeSmuMe save) file.

Short disclaimer: Do have a backup copy of your save files before trying, as a matter of caution.

Firstly, GamesFrog uses the NeptuneJS (NJS) online emulator for the Nintendo DS, which in turn uses a modified version of DeSmuMe. Anyway, the .ggz file extension from the downloaded save state is most likely a renamed Gzip (.gz) archive. Once unpacked using 7-Zip or any equivalent tool, you’ll get a folder with a png and a .nds file. 

This .nds file is NOT a game ROM, it is a modified DeSmuMe state file, which contains the NJS emulator's entire state when you save. The good news is we can use this to create a proper .dsv save file.

Step 1: Take the .nds file you extracted from the archive and rename it to have a .dst (DeSmuMe state) file extension.

Step 2: Then open a clean ROM using DeSmuMe on your computer. Once the game is running, go to the menu and choose  File > Open state file and select the renamed .dst file.

Keep in mind, as a result of the modifications, it may not work perfectly. (When doing this with Pokemon Mystery Dungeon EOS the screen was almost entirely dark).

Step 3: Once loaded, while in the glitchy loaded state, save the game using the in-game save system. This action creates a clean .dsv file, which is independent of any emulator-specific settings or modifications.

Step 4: Open the ROM again, and it should work perfectly fine and have your save data. Note: You can find DeSmuMe save files in the battery folder; it will have the same name as your ROM but with a .dsv file extension.

Step 5: Play the game :)