Is it permissible to appoint a successor if the imam is unable to complete the prayer, mentioning the views of the four madhhabs?

If an excuse arises for the Imam (such as remembering a hadath or impurity, nosebleed, fear of loss of property/life, or inability to perform a pillar), it is sunnah for him to appoint someone else to complete the prayer. Umar, may Allah be pleased with him, appointed Abd al-Rahman ibn Awf after he was stabbed. Substitution is obligatory in the Friday prayer because it is not valid except in congregation.