Finding the trunk may also make Harry more determined. If there are any signs of her fight against the dark forces in the trunk, like a plan she was making or a charm she was developing, it could fuel Harry's own determination to defeat Voldemort and protect the wizarding world.
Another possibility is that it just randomly appears one day. Magic in the Harry Potter world can be unpredictable. One morning, Harry wakes up and there it is at the foot of his bed. Or maybe a magical creature, like a house - elf that knew his mother, decides to bring the trunk to him. The house - elf could have been sworn to secrecy until the right moment when it senses that Harry is ready to discover his mother's secrets.
There could be her personal diaries. Maybe she wrote about her time at Hogwarts, her friendships, and her early days with James Potter.
It might make him see them more as real people. Before, they were just an idea of parents, but the trunk could contain things that show their personalities, like their sense of humor or their interests.
Perhaps there could be her old Hogwarts textbooks. They might hold some special notes or spells that she had discovered during her time at school.
There could be some of his parents' old school things like their Hogwarts robes, wands (if they were allowed to keep them), and textbooks. Maybe there are also some love letters between his parents or photos of their time at Hogwarts.
The learning trunk might offer him a more personalized learning experience. For example, if he's struggling with a certain spell, the trunk could provide a step - by - step guide or even a magical tutor in the form of a spell - casted projection. Also, it could give him the opportunity to study at his own pace without the distractions of a classroom. He can focus on the areas he's most interested in or needs to improve on, like advanced transfiguration or advanced defense against the dark arts.
It might make his relationships more intense. If his mother's temper was passionate, he could be very intense in his friendships. He might be the kind of friend who is extremely loyal and gets very angry if his friends are wronged.
It completely flips the typical mother - son relationship. Instead of the usual love and support, there's tension and hostility. It can make Harry more of a rebel, going against his mother's wishes or values.
One way Harry Potter might act like his mother in the fanfiction is through his nurturing side. His mother was a loving and caring person. So, Harry could be seen taking care of his friends when they are sick or in trouble. He might also be very inclusive, making sure that no one feels left out, similar to how his mother would have treated people around her. This could also be shown in his relationships with his Hogwarts classmates, where he goes out of his way to make everyone feel welcome and valued.
In the 'Harry finds Lily's school trunk' fanfiction, it could be that Harry stumbles upon the trunk and inside he finds a diary. Through this diary, he gets to read about Lily's adventures at Hogwarts, her friendships, and her early encounters with Snape. This would be a great way to explore Lily's character more fully from Harry's perspective.