When you generate a wallapper, you press the tick icon to save it, so you can set it as a wallpaper later, but I don't think you can save it as an image file and send it.
You can't save it to media folder. The app I use to save Zedge wallpapers I have bought, which you can only apply and not download, is called wallpaper saver. It is excellent for backing up those Zedge wallpapers for me. I tried to use it to save my AI wallpaper but it just saved an Android symbol. So that didn't work. Which makes me think it can't be saved.