He didn't have to "covert" to "become" anything.
I said nothing about covert activity. I was referring to conversion.
Here is an example of the word conversion: "So, being sent on their way by the church, they passed through Phoenicia and Samaria describing the conversion of the Gentiles, and they caused great joy to all the brethren." (Acts 15:3 NKJV)
Jesus had already established that Peter was not converted as well as the Jews in general.
For example Jesus quoted Isaiah: "For this people's heart is waxed gross, and their ears are dull of hearing, and their eyes they have closed; lest at any time they should see with their eyes, and hear with their ears, and should understand with their heart, and should be converted, and I should heal them."
Conversion is referring to spiritual understanding which is not possible without God's Spirit.
A person must be converted from being carnally minded to being spiritually minded.
Paul explained, "For those who live according to the flesh set their minds on the things of the flesh, but those who live according to the Spirit, the things of the Spirit." (Romans 8:5 NKJV))
Peter instructed his brethren, "Repent therefore and be converted that your sins may be blotted out, so that times of refreshing may come from the presence of the Lord..." (Acts 3:19 NKJV)
To be converted is referring to a change in character from what we are by nature to what Jesus is. It requires God's Spirit.
So in the world today there are those who have been converted and there are those who have not been converted.
Conversion is the most important aspect of NT teachings.