According to the textbook, sleep consolidates our memories by reactivating recent experiences stored in the and then shifting them for permanent storage elsewhere in the cortex.

The correct answer is the hippocampus.
The hippocampus is the part of a mammal's brain which is responsible for keeping short-term memory and then turning it into long-term memory. So here, we can see that sleep transforms our short-term memories stored into our hippocampus into permanent memories stored somewhere else. 

Bob: coke is baby pandas.jim: what? how do you figure that coke is baby pandas? bob: because this book says so.jim: how do we know the book is correct? bob: because it says that coke is baby pandas.jim: how does that prove the book's accuracy? bob: because it's statement involving coke and baby pandas is correct, therefore it is accurate.jim: how do we know that it's correct? bob: because we have concluded that the book is accurate, and therefore the statement is correct.therefore, coke is baby pandas.