The appointment of the imam may take place in one of three ways: either the preceding caliph designates him; or those qualified to decide and bind in the community agree upon him; or he assumes the position by force and domination.
An example of the first is Abu Bakr’s designation of Umar as caliph. (1) If someone were to ask: “Who appointed Abu Bakr as successor?”
We say: The Messenger of Allah, peace and blessings be upon him, appointed Abu Bakr as his successor. However, someone may object: “Where is the explicit text from the Messenger, peace and blessings be upon him? Did he say to Abu Bakr, in these very words, ‘You are my successor over my nation’?” No. Yet some have said that he appointed him by indication—that is, he performed acts indicating that Abu Bakr would be caliph after him. Others have said instead that his caliphate was established through the consensus of those qualified to decide and bind, since the Companions, may Allah be pleased with them, unanimously agreed upon it.
The correct view is that his caliphate was established by textual proof, whether explicit or by implication and indication.
First, during his final illness, the Prophet, peace and blessings be upon him, appointed Abu Bakr to lead the people in prayer. When they called for Umar, may Allah be pleased with him, he became angry and said: “You are like the women around Joseph,” referring to his wives who had called for Umar. He then ordered that Abu Bakr be summoned, and he came; thus, he appointed him to lead his nation in prayer. (2)