A party cannot unilaterally go and replace an item and then come claiming the cost - whatever happens. So these bozos are in the wrong.

The school, as it happened on their property, has a responsibility.

You cannot and must not deal with the child. He is not an adult. You can therefore ignore everything he says. The parent(s) are the only ones you should be dealing with.

If the kid calls up, tell him that clearly. And add that, if he's not mature enough to behave correctly in the school yard then how can he be responsible enough to handle this situation.

For anything to be done, the jacket cannot simply be replaced but should be assessed, the age considered and then any next steps can be taken; if the new jacket has been purchased already then they are absolutely in the wrong.

It sounds like his mother does not like confrontation.

Now get your husband on the case