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.