The built-in file manager should allow you to do that. I have tested this option on Android 4.4.x Kitkat and Android 5.1.1 Lollipop. It worked as it should. I have used the built-in File Manager. However, if you can't do it with the default app, then I recommend using a File Manager from the Play Store called ES File Explorer. Install the application, then long tap on a file/folder and use Copy. Then browse to the SD card by tapping on the bar with the path until you reach the desired destination. Use Paste here and that's it.