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In WPF, the element that has keyboard focus will have IsKeyboardFocused set to true. The default value of Popup.IsKeyboardFocused is false and read only property, so you can't get focus on the popup. You could use Keyboard.Focus(targetedElement) in the event to make it to be focused. You can refer to document Keyboard Focus and sample in the thread: WPF Popup tab key bug for more info.
Keyboard Focus
Thanks.