Where does gravitational potential energy reside?

n order to lift a body, energy is required. The potential energy increases. However, where exactly does this energy reside once the body is lifted? This is a natural question and it seems to be a reasonable question. The textbooks deal with it in different ways. Some say that the potential energy is located in the body that has been lifted. According to other sources it is localized in the system earth-body. In a third category of books, it is confirmed that the energy is stored, but nothing is said about the place where it is stored. Finally, there are books, especially for the university, in which the facts are formulated in such a way that it does not come to our mind to ask the question. A better answer is that the potential energy is stored within the gravitational field. However, the question arises as to where in the field the energy released by the lifted body can be found. The answer to this question is somewhat involved. One can only specify the extension of an area in which positive and negative energy density changes occur as the body is lifted.