In the eyes of God, all sins are forgiven upon conversion, according to the Sunni tradition. This can be proved with any work on Aqeedah and from numerous ahadeeth of the Prophet (s).
However, this does not mean that the justice system in which where one lives needs to take the conversion into account. Muslims must live by the laws of the land in which they reside and respect the legal system, especially with regards to matters of justice. The conversion has no bearing on the justice system.
The conversion means that spiritually, the person has made peace with God and the Message of His Prophet (s) and has accepted the Truth, and promised to live a noble way of life in this world and hope for salvation in the Hereafter.
One should consult legal counsel for such situations and act in accordance with the law.