Does a judge appointed by an Imam remain in office if the appointing Imam dies?

Primary text

The judge does not vacate his office upon the death of the Imam who appointed him. This is established because the Rightly Guided Caliphs appointed judges during their time, and those judges were not dismissed upon the death of the appointing Caliph. Furthermore, dismissing the judge upon the Imam's death causes harm to the Muslims, as the governance of the regions becomes suspended, and the legal affairs of the people halt until the next Imam appoints a judge, which constitutes a great harm.