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Fortunately, he exercised his free will, and stopped the practice out of love of God. He refrained from habitual behavior because he developed an understanding, and love for God he didn’t have before.

An unbeliever cannot stop sinning unless God so wills it. This comes directly out of the Catholic Council of Orange:

CANON 4. If anyone maintains that God awaits our will to be cleansed from sin, but does not confess that even our will to be cleansed comes to us through the infusion and working of the Holy Spirit, he resists the Holy Spirit himself who says through Solomon, "The will is prepared by the Lord" (Prov. 8:35, LXX), and the salutary word of the Apostle, "For God is at work in you, both to will and to work for his good pleasure" (Phil. 2:13).

CANON 7. If anyone affirms that we can form any right opinion or make any right choice which relates to the salvation of eternal life, as is expedient for us, or that we can be saved, that is, assent to the preaching of the gospel through our natural powers without the illumination and inspiration of the Holy Spirit, who makes all men gladly assent to and believe in the truth, he is led astray by a heretical spirit, and does not understand the voice of God who says in the Gospel, "For apart from me you can do nothing" (John 15:5), and the word of the Apostle, "Not that we are competent of ourselves to claim anything as coming from us; our competence is from God" (2 Cor. 3:5).

CANON 8. If anyone maintains that some are able to come to the grace of baptism by mercy but others through free will, which has manifestly been corrupted in all those who have been born after the transgression of the first man, it is proof that he has no place in the true faith. For he denies that the free will of all men has been weakened through the sin of the first man, or at least holds that it has been affected in such a way that they have still the ability to seek the mystery of eternal salvation by themselves without the revelation of God. The Lord himself shows how contradictory this is by declaring that no one is able to come to him "unless the Father who sent me draws him" (John 6:44), as he also says to Peter, "Blessed are you, Simon Bar-Jona! For flesh and blood has not revealed this to you, but my Father who is in heaven" (Matt. 16:17), and as the Apostle says, "No one can say 'Jesus is Lord' except by the Holy Spirit" (1 Cor. 12:3).

CANON 23. Concerning the will of God and of man. Men do their own will and not the will of God when they do what displeases him; but when they follow their own will and comply with the will of God, however willingly they do so, yet it is his will by which what they will is both prepared and instructed.

Council of Orange

And if you would like a scripture verse then please note the following which states the same thing:

Joh 1:12-13 But to all who did receive him, who believed in his name, he gave the right to become children of God, who were born, not of blood nor of the will of the flesh nor of the will of man, but of God.

We are born again 1) not by physical heritage, 2) not by any action we can take, 3) and certainly not because we will it because we come to some understanding. We are born of God by His grace and His alone.

In your example, if a Muslim were to become a Christian, it is only because God has so enlightened His heart and brought him to the point where he will repent. It isn't because of something he's done by his "will". As Canon 23 states, man does their own will-not God's will. God changes the heart to comply with His will.

Any other view is not the true faith according to the Council of Orange. I happen to agree with their analysis.