Controversial issues and their resolutions.

You can simply agree to a draw and start a new game in a friendly manner. If both players are very serious, then replay the battle until one wins. As for those who insist on continuing the current battle, they can take screenshots or record the battle on video. However, it can be very difficult, sometimes almost impossible, to perfectly replicate a battle. Factors such as morale drops or resistance triggers are very hard to predict.
In general, it's not worth playing with those who demand something... Of course, if it's a tournament, there's no other choice... But in a tournament, there's a judge who should resolve the issue.