The theological basis for conversion lies in the truth of the "atonement."
Although man lapses into sin, the truth of the atonement remains. When men turn to God in repentance and faith, the effects of the atonement - reconciliation and forgiveness - avail.
Paul expresses the act of conversion in this way: "Turning to God from idols to serve the living and true God" (1 Thessalonians 1:9).
Also, "to open their eyes (the Gentiles), and to turn them from darkness to light, and from the power of Satan unto God, that they may receive forgiveness of sins, and inheritance among them which are sanctified by faith that is in me" (Jesus) (Acts 26:18).
Jesus instructed Peter to get back into ministry after he repented of his denial. If Jesus had not given Peter this command, many people might have doubted that Peter should be in a position of leadership. Peter himself must have doubted whether or not he was fit. After Jesus' resurrection, the Lord again admonished Peter three times to serve Him by ministering to His sheep.
In Luke 22, Peter's faith was shaken and he denied the Lord but did not reject Him. Jesus' admonition to Peter was that when he turned back again to Him (converted), he was to strengthen the brethren.
