PanelBが内部クラスならできるよ

public class FrameA extends JFrame
{
 JMenuItem menuItemForB = new JMenuItem();
 public FrameA(){
  menuItemForB.addActionListener(
   new ActionListener()
   {
    public void actionPerformed(ActionEvent e)
    {
     panelB = new PanelB(){
    }
   }
  );
 }

 public class PanelB extends JPanel
 {
  public PanelB() //frameAの参照を引数で渡す[RRR]
  {
   //FrameA.thisで呼ぶ
  }
 }
}