Judge Moore has the official authority to do it.
I believe you are correct in arguing that there is no issue with Moore's first amendment rights as a citizen.
But I also believe it is entirely appropriate in his official capacity to place a monument to what is undeniably a moral basis of our law.
He may be in charge of the building overall, but his actions as building custodian are subject to the laws of the land. He is the caretaker of public property. He must manage the property in such a way as not to conflict with the Constitution.
The legal system of the United States is based on a rich variety of historical precedents. The fact that the Old Testament is one of those precedents is not an excuse for placing avowedly religious artwork in a public building.