As long as you have registered a Duelist Account, you can continue your Duel Generation progress, with your Cards and Decks, on any advice with Duel Generation installed.
It is highly recommended you log out of your account on the current device before transferring your data to the new device.
On the new device, log out of the current account then click on the Avatar image in the bottom left corner of the Main Menu screen. From the resulting pop-up menu choose the LOG IN option. Enter your User Name and Password and select the option to download your game data from the server.
And that’s it! Always make sure to log out of any device that could be used by people other than you.