Isn't it right to say "on the old spot" instead of "in the old spot" because it is to put something on the place?
Good question! While the preposition "on" is generally used for objects which are above the surface of something else, and "in" is used for objects contained inside something else, here is a totally different case. The preposition "in" here is used to denote the location of an object. So "in the old spot" is the correct sentence here, because the old spot is where the stool will be located. While other prepositions like "at" may also denote location, it can be hard to know which preposition to use since there is no exact rule and prepositions are very idiomatic. Here's a few examples of the preposition "in" meaning location: Ex: He won't be back for a few days because he is in California. Ex: I have sand in my eye!