If someone is appointed as imam's deputy during prayer, should he start recitation anew or continue from where the imam left off?

Hazrat Ibn Abbas (may Allah be pleased with them both) narrates that when the Messenger of Allah (peace and blessings be upon him) came to Hazrat Abu Bakr during the prayer in his final illness, he started the recitation from the point where Hazrat Abu Bakr had reached.

Hazrat Aamir says that if a man's ablution breaks during prayer and he appoints someone else to lead as imam, then the recitation and takbeer of that person are sufficient for him.

Hasan, regarding the person whom the Imam appoints to lead, says that if he wishes, he may recite from where the Imam had reached, and if he wishes, he may recite from another surah.