DraStic

Is there a way to transfer my save game files from Desmume version 0.9.11 to Drastic version r2.5.0.3a on my phone?

Copy them to sdcard/DraStic/backup. Make sure the file name is the same as the ROM name, except with the .dsv extension.

This only applies to in-game save files (with extension .dsv), not savestates.

I put the .dsv file for the game in the backup folder but the game doesn't seem to find the save file it only tells me to start a new game. The .dsv has the exact same name as the ROM.

Could you upload the .dsv file along with the game's name/region?

Harvest Moon DS / USA

Strange, I have no problem loading that save file.

Are you sure the file name is completely exact except the extension, as in has the same capitalization of letters and any spaces?

Yes the name is exactly the same. Im going to try to transfer a dsv for another game and see if that game will work. (Edit. Other games dsv files work except for the harvest moon one.

And you're sure it's the same ROM file used with DeSmuME and DraStic?

Yes I copied and pasted the ROM from my laptop to my phone.

The save works for me, too.
I have seen cases where filenames were slightly changed when copying a file to an Android device.
You can try using an app like ES File Explorer and copy/paste the filename from the ROM to the save again, just to make sure.