It seems that there are many ways to achieve this. In my case I choosed to do a backup in iCloud and just restore it on the new phone and it works perfectly for me.
But to make this work you have make sure that your Line app is linked correctly the your iCloud account.
- In the LINE app of your old phone tap "Home" and then the top right gear icon for "Settings". Then go to "Account"->"Apple" und tap the "Link" button.
- After that you have to backup the chat history from the old iPhone to the iCloud. You can do this in the same Settings menu as before. This time go to "Chats"->"Chat history Backup"->"Back Up now"
- Now just log in into the LINE app on your new phone and go to the "Settings" menu and tap on “Restore chat history.”. Thats it!