If God truly imputed Christs righteous in a person then they will also DO righteousness.why does God Impute his righteousness? Because we are unrighteous,
That is where the false doctrines get exposed that say despite being made righteous by Christs imputed righteousness they still walk in unrighteousness.
Here is the proof a true conversion…
1 John 2:29
If ye know that he is righteous, ye know that every one that doeth righteousness is born of him.
1 John 3:7
Little children, let no man deceive you: he that doeth righteousness is righteous, even as he is righteous.
1 John 3:10
In this the children of God are manifest, and the children of the devil: whosoever doeth not righteousness is not of God, neither he that loveth not his brother.
So you will know a tree by his fruit.