What is the authenticity of the chain of transmission for Abu Bakr's will to Umar, and what are its sources?

Umar ibn al-Khattab, may Allah be pleased with him, feared for the Muslims discord after his death, so he consulted the senior Companions and people of authority regarding the selection of his successor. After individual consultations with a number of them, he observed their agreement on the competence and virtue of Umar ibn al-Khattab. Abu Bakr then announced his choice of Umar, and all the Companions and people agreed to it and pledged allegiance to Umar with obedience and loyalty. This confirms that imamate and legitimate rule are not established except with the consent of the Muslims.