If he usually goes to the supermarket with you, tell him to make a list of what you should buy. As he collects each item, help him cross it off the list. Another fun activity that requires sequential thinking and good organization is a scavenger hunt. He is old enough to navigate the mall alone or with friends, and this game could be fun. Your hunt could include tasks like finding out and recording the color of a hat in the window of a certain store.
After starting him off with fun activities like these, encourage him to make lists for more mundane things: chores on Saturday, the things to do after school each day, etc. At the same time you could model personal organization skills for him by making your own lists of what he would like in his school lunch or for dinner.
Now move into the school area. Make an appointment with the teacher (a phone conversation is fine) to discuss her perception of why he "forgets" everything. As a teacher, I would suggest that your son write down assignments and keep a homework notebook. It may be necessary to ask the teacher to initial it each day to verify that he is using it. At home, he needs to check off each thing as he does it. You may need to give him the OK to check it off.
If your child is already writing things down and you believe that his work habits are good, ask the teacher about having the school do a formal assessment of his short and long term memory.