What is the ruling on a congregational prayer where an incidental matter caused the Imam to leave, and he appointed a follower as his successor who had already uttered the opening Takbir and re-entered the prayer?

Firstly, it is permissible for the Imam to appoint someone to deputize for him in leading the prayer. The first Imam should have presented the most knowledgeable among the worshippers in the rulings of prayer.

Secondly, the second Imam erred by exiting his prayer, which he had entered as a follower, in order to enter as a new Imam with a new opening takbir. It would have sufficed for him to change his intention from following to leading without invalidating his first prayer. However, he is excused due to his ignorance. His second prayer is valid because he entered it with a correct opening takbir.

Thirdly, the fact that the congregants entered the prayer with the first Imam and then completed it with the second Imam, who uttered the takbir for ihram (definition) after them, does not invalidate their prayer. There are indications in the Sunnah (definition) that attest to the validity of this, such as the story of Abu Bakr leading the prayer and then the Prophet, peace and blessings be upon him, joining him, as well as the hadith (definition) of Abu Bakra that the Prophet, peace and blessings be upon him, returned to the prayer with his head dripping after he had left and abandoned the congregants. The congregants are not required to repeat the opening takbir.