Final answer:
The statement is false; after Muhammad's death, the leadership of the Muslim community passed to the Rightly Guided Caliphs, and Mehmed II was a later Ottoman Sultan.
Step-by-step explanation:
The statement that Mehmed II was chosen to be the leader of Islam after the death of Muhammad is false. After the death of Prophet Muhammad in 632 CE, the Muslim community chose Abu Bakr as the first caliph, followed by 'Umar, 'Uthman, and 'Ali, in a period known as the reign of the Rightly Guided Caliphs. Mehmed II, also called Mehmed the Conqueror, was born much later and became the Sultan of the Ottoman Empire, laying siege to Constantinople in 1453.