This popup cannot be opened by the keyboard and cannot be closed by the keyboard, it is symmetric. It is similar to say unfocusable Button which cannot be navigated nor pressed by the keyboard.
You probably need to read something about the UI accessibility principles before fixing such bugs, because what you stated above just opposites to them.

You missed the point that we are not an application, but a library which provides different things to the applications, it is up to the application to use non-focusable components.

What???
AWT is not a library, it's a *toolkit*. And the Choice AWT component implements javax.accessibility.Accessible interface which means it "is a" Accessible component.
AWT isn't simply a library to draw components.

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