Accessing @SessionCoped @Named beans from a HttpSession

Question

I have a JSF Mojarra 2.3.9.SP02 application and a couple of beans there. One of the beans looks as follows:

@Named("unterlagenBean")
@javax.faces.view.ViewScoped
public class UnterlagenBean extends KauferBaseBean implements Serializable {
     // code here
}

The parent class looks as follows:

public abstract class KauferBaseBean {

    @Inject
    @javax.faces.bean.ManagedProperty(value = "#{kauferSessionContainer}")
    private KauferSessionContainer kauferSessionContainer;

}

And the KauferSessionContainer looks as follows:

@Named("kauferSessionContainer")
@SessionScoped
public class KauferSessionContainer extends AveSessionContainer {
}

Now, I have a servlet, from which I want to access the KauferSessionContainer, if there is a HttpSession, and if the KauferSessionContainer is in this session.

How can I do this? Simply trying

request.getSession(false).getAttribute("kauferSessionContainer")

delivers null