I have an older child with ASD and dyspraxia who is still incredibly forgetful. But he is also now very organised at school, and I think this is to do with hyperfocus and habits. So once he does something regularily and it is associated with some other habit he finds it very easy to remember.
So for example he has no difficulty remembering to put his travelcard in the same little drawer in the hall, and putting his homework in his bag now because he never deviates from this pattern. This comes at a cost, which he refuses to take any books out of his bag except to do homework and then immediately puts them back again, which makes his knapsack enormously heavy!! But he says if he tries to make a plan, he forgets something, so the habit stays.
At this age, only 7 I would say that prompts are the way to go, and little things like perhaps never taking his jumper off (is school incredibly hot?) or always tying it round his waist (you could practise this) if he does. And putting his pens back in a box always, again practise at home so it becomes like a physical habit. But homework should be prompted by the teacher and he personally should be prompted, not just a generic prompt to whole class, until he gets into the habit (and he will, that physical habit of walking up and handing it in, will remain in his memory banks) Habits are also reinforced by similar journeys, so if you do the same journey in the house every time you do a habit it is quite easy, otherwise they tend to go into "fugue" and wander around and have absolutely no idea why they have headed upstairs, to a room, and what they were looking for.
It is to do with processing, the processing of spoken instructions, which probably will not sink in, whilst he is thinking or concentrating on something else. If you explain this to the teacher that however many times she says something it is physically not processed by his auditory memory, she might see why he cannot remember or do what she asks. It needs a physical association or series of steps to stay in his brain.
HTH