The built in texture converter in DAZ Studio might do V3 to V4 then you could use the V4 version on Genesis. Never tried that myself but it is built in now.
It doesn’t work that way. Gen3 textures can’t be loaded onto Gen4 or 5 characters, and you’d need a character with access to both Gen3 and Gen4 UVs to use the map transfer util that way.
To convert Gen3 textures, you will need Texture Converter 2… or lots of patience to do it manually onto a V4 UV layout, which I don’t think anybody has that kind of patience.