You could try to assess where he is in terms of appreciating the difference between 'mine' and 'not mine' when you see he has some item in his possession that you know comes from school. It may well be that he really hasn't yet got to the stage where he can understand this major difference. He really is very young still.
He is only at the start of a process (of understanding this difference between mine and yours) that he should have completed by age 7. If you ask him whose post-it notes these are and he says they are his, then you can gently probe and find out how they came to be his since he did not buy them and you did not give them to him. Just ask for assessment purposes initially, and you can interject the comment that perhaps he wishes an item was his but it isn't really his just because he wishes it. Remember though that children his age believe in Santa and magic.
Once he gets the idea that things he buys or things you give him are his (through using a little money to buy things he fancies, without comment from you even if you think he is choosing rubbish) then you can ask him who owns various things at home, his toys or your wooden spoons or dad's hat or the cat's bowl, etc. Gradually he will develop an understanding. Also, don't force him to share things that he owns, and if he asks for things that another child doesn't want to share when playing, help him to accept that 'no' answer and explain that everyone has a right to decide not to give, and while he is disappointed, he might prefer not to share or give too, one day.
Try to not make remarks about lovely things that other people have. Make sure you talk up your own stuff and his. Don't disparage other people's possessions, just don't bring up the topic. You never know how small children are interpreting or comparing when you talk about things other people have.