But we don't know anything about Jay. There has been a lot of talk of possible affair between Jay and Jenn, but it could be anyone. He could have made a pass at Hae and she threatened to tell Stephanie. He could be the psychopath who just wanted to get away with it.
Stephanie's parents disapproved of him, that could be a factor.
None of this would help obviously but he might have a motive no one knows about.
Similarly, Adnan could have argued with Hae the night before, no one knows what took place.
The timelines are confusing, but if the murder didn't take place at 2:36 then the Asia letter is irrelevant - but Hae would still have had to have been intercepted before she picked her cousin up from school.
If it did occur later, then there's no way Jay could pick Adnan up and do all that before getting him back to school for 4pm.