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A couple of observations on the above:
"The president has full authority" ---- Won't argue too strenuously, tho I would think there must be some caveats within that power.
But then, it is a "president".......not an "ex-president".....who has that power.
For an ex-president to have it then that appears to be a co-presidency. Or bi-presidency.
And in that, I am really really skeptical.
When the previous guy goes.....he loses a lot.....a friggin' LOT....of his prior power.
As it should be.
And too, I like the poster's comment above who observed that the succeeding president could simply re-classify anything the first guy de-classified.