The only way to transfer your game progress from one iOS device to another is to connect your game to the iOS Game Center.
To connect to Game Center:
Tap on ‘Settings’ icon for your iPhone
Search for ‘Game Center’ and tap on it
Enable Game Center in the phone and create a profile (if you don’t already have one)
Open Legend of Solgard app
Tap on the Settings icon in the top left corner
Tap on ‘Connect’ (green button)
The app will automatically try to connect to Game Center with your logged in account
When you play on the new device simply open the game, go to the settings menu and log into Game Center to retrieve all your progress.