There is no right invented from "thin air". The money was taken premised on a criminal conviction. The conviction was reversed on review, which means it was not a valid conviction (this isn't a pardon or other act negating the effect of a valid conviction, it's a legal act determining the validity of the conviction.)

The premise which justified taking the property was invalid, thus the state had no legal basis to deprive the victim of property.

Now, if this was a question of the personal liability of agents of the state in taking the money, the fact that they had a reasonable good faith belief that they acted based on a a valid legal premise would probably be a valid point, if governmental immunity didn't make it moot in the first place. But this isn't about that.