Stopping the Storyboard can be done in the code behind, or the xaml, depending on where the need comes from.
If the EventTrigger is moved outside of the button, then we can go ahead and target it with another EventTrigger that will tell the storyboard to stop. When the storyboard is stopped in this manner it will not revert to the previous value.
Here I've moved the Button.Click EventTrigger to a surrounding StackPanel and added a new EventTrigger on the the CheckBox.Click to stop the Button's storyboard when the CheckBox is clicked. This lets us check and uncheck the CheckBox when it is clicked on and gives us the desired unchecking behavior from the button as well.
<StackPanel x:Name="myStackPanel">
<CheckBox x:Name="myCheckBox"
Content="My CheckBox" />
<Button Content="Click to Uncheck"
x:Name="myUncheckButton" />
<Button Content="Click to check the box in code."
Click="OnClick" />
<StackPanel.Triggers>
<EventTrigger RoutedEvent="Button.Click"
SourceName="myUncheckButton">
<EventTrigger.Actions>
<BeginStoryboard x:Name="myBeginStoryboard">
<Storyboard x:Name="myStoryboard">
<BooleanAnimationUsingKeyFrames Storyboard.TargetName="myCheckBox"
Storyboard.TargetProperty="IsChecked">
<DiscreteBooleanKeyFrame KeyTime="00:00:00"
Value="False" />
</BooleanAnimationUsingKeyFrames>
</Storyboard>
</BeginStoryboard>
</EventTrigger.Actions>
</EventTrigger>
<EventTrigger RoutedEvent="CheckBox.Click"
SourceName="myCheckBox">
<EventTrigger.Actions>
<StopStoryboard BeginStoryboardName="myBeginStoryboard" />
</EventTrigger.Actions>
</EventTrigger>
</StackPanel.Triggers>
</StackPanel>
To stop the storyboard in the code behind, we will have to do something slightly different. The third button provides the method where we will stop the storyboard and set the IsChecked property back to true through code.
We can't call myStoryboard.Stop() because we did not begin the Storyboard through the code setting the isControllable parameter. Instead, we can remove the Storyboard. To do this we need the FrameworkElement that the storyboard exists on, in this case our StackPanel. Once the storyboard is removed, we can once again set the IsChecked property with it persisting to the UI.
private void OnClick(object sender, RoutedEventArgs e)
{
myStoryboard.Remove(myStackPanel);
myCheckBox.IsChecked = true;
}