Who purified the Companions, and how did purification continue after the Prophet?

We believe that the Beloved Prophet ﷺ performed the task of Yuzakkihim, purification, himself, on his Companions; hence, the Companions reached the level of excellence which no other human can achieve till the end of time. Allah's Messenger ﷺ led by his own example of the best morals, and the Companions followed him in each and every aspect and taught those ethics, or Khulq, to their followers, and so on.

The ones who adjoined the company of the Beloved Prophet ﷺ had the opportunity to learn from him, and the Beloved Prophet ﷺ testified on their behalf as he said, "The best mankind is my generation." [Sahih al-Bukhari] They were the ones who had the best morals and excelled in this world and the hereafter. They loved for the sake of Allah and hated for the sake of Allah, their end goal was to please Allah, and they definitely succeeded in that mission.

That was the outcome of the Prophetic teaching and purification. Even after the Beloved Prophet ﷺ left this world, the Companions continued his mission till the end of their lives.

Referring to the first objective of the mission, which is to recite the verses of the Qur'an and teach the Book, it is obvious that the Qur'an had to be taught. Even though the Arabs were fluent in the Arabic language and known for their eloquence, the verses were explained and the meanings taught by the Beloved Prophet ﷺ. Allah's Messenger ﷺ imparted the knowledge of the Qur'an to the Companions, and then the Companions taught the Tabi'een, the ones who followed the Companions, and the Tabi'een educated the Taba Tabi'een, the ones who followed the followers of the Companions; thus, the process continued.

When the objectives of reciting the verses and teaching the Qur'an were carried forward by the Companions of the Beloved Prophet ﷺ, the other tasks of the mission, such as teaching wisdom and purification, were also taken over by them. Hence, the process continued just as the first and the second objective of the mission.