Your document concerns the validity of the cede in 1836, not military movement and occupation in 1861.
And you of course, know that.
Produce the military order for Anderson to move into Ft. Sumter.
The document clearly states that South Carolina ceded to the United States "all the right, title and claim of South Carolina to the site of Fort Sumter and the requisite quantity of adjacent territory..." That means they had no legal claim to it.
But you knew that.
Even had the Southern session had been legal, that would not have changed ownership since South Carolina had no legal claims to the territory. It would, at best, become foreign territory and remained the property of the U.S.
But you knew that, too.
According to the Constitution only Congress can dispose of federal property, like forts and the like. Again assuming for the sake of argument that the Southern secession was legal, it would have taken an act of Congress to transfer ownership from the U.S. to the confederacy.
You would know that as well, assuming that you aren't a complete idiot.
Produce the military order for Anderson to move into Ft. Sumter.
Anderson commanded all the military facilities in the Charleston area. That included Fort Sumter. No military order was necessary for him to move. But he did have verbal authorization from Don Carlos Buell to take whatever steps were necessary to ensure the safety of his men. That provided all the authorization he needed.