Your phones do not need to be rooted, but if they are you might want to install Superuser by ClockwordMod as I had problems with a different Superuser app.
1. Install the free Helium by ClockworkMod app on both old and new phones.
2. Start Helium app on old phone. If your phone is rooted then skip to step 7.
3. On your computer install Helium Desktop.
4. Connect phone to PC via USB.
Problems here may indicate a driver issue. In the Windows Device Manager you should see your Android device listed as shown below. If it has a yellow exclamation mark you need to install the correct driver.
6. Disconnect USB cable.
7. In Helium app menu choose PC Download. This should display the Helium Server screen, with a big green power button. Note the URL displayed.
8. Use a web browser on your PC to access the URL listed in the app.
10. You've finished with the first phone, so exit the Helium app.
11. Follow steps 2 to 8 again, but with your new phone.
12. On the web page choose Restore, and point it to the zip archive you saved earlier.
13. Candy Crush should now be playable on your new phone.