Did the Messenger, peace and blessings be upon him, order the collection of the Qur’an?

The Qur'an was not compiled into a single mushaf during the time of the Prophet, peace be upon him. The Companions used to write it down using the available means they had. Then, Abu Bakr Al-Siddiq compiled it based on the advice of Umar ibn Al-Khattab after a large number of Qur'an memorizers were martyred in Al-Yamamah, and Zayd ibn Thabit undertook this arduous task. As for the reason it was not compiled during the Prophet's lifetime, it was out of fear that something might be abrogated by revelation. When the revelation ceased with his death, Allah inspired the Rightly Guided Caliphs to compile it.