This British professor gets it wrong:
[Hyperreality refers] to the idea that it is no-longer possible, in a media-saturated world, to distinguish between what is real and what is not ... Hyper-reality, therefore, is a situation in which nothing and everything is "real"; it is a situation in which we have lost the ability to distinguish reality and fiction.
The whole point of this thread is that it is eminently "possible, in a media-saturated world, to distinguish between what is real and what is not." That is Baudrillard's point, too. He is calling on us to recognize and preserve meaning.
Baudrillard says that in a state of hyperreality, the term (or icon, or symbol) has broken completely free of its meaning and is now free floating.
We can map the stages: Lincoln becomes an icon, then an image, then a motif, then an amusement, then an attention-getting device. In the end, Lincoln is a totally senseless, even absurd, figure:
A child dresses like a a vaudeville comedian in order to recite the Gettysburg Address.
Lincoln and a businesswoman share a copy of the Wall Street Journal.
Lincoln helps a shopper buy golf clubs.
Lincoln helps photograph tourists at the Kremlin.
Lincoln drops by the office for a chat.
You have become Lincoln but still look like yourself.