Вольная трактовка:
1. On my way to school, I suddenly realized I left my report behind.
2. Going to school, I recalled that I forgot my report at home.

(1) LEAVE BEHIND can be anywhere - the café where you picked up your coffee, the car/bus you rode to school in, your friends house, where you stopped to pick up your classmate, etc. The Russian text specifies that you left the report at home. (2) GOING TO SCHOOL doesn’t work here because it sounds like BECAUSE I GO TO SCHOOL. If you want to make it current, you would say AS I WAS GOING TO SCHOOL, but that doesn’t sound idiomatic because in that context, we say ON MY WAY TO SCHOOL. Also, RECALL is used for calling up information that is latent in your mind - this would not qualify.

1. Если в контексте прямо говорится, что ученик вышел в школу из дома, то конструкция "leave behind" подразумевает вполне определенное место — "home". 2. Оборот "going to school" в текущий/определенный момент времени можно перевести русским выражением "идя в школу". 3. Если отчет был подготовлен дома давно, то горе-учащийся мог вполне забыть о нем, и потому глагол "recall" совершенно уместен, п-ку будет отражать реальное положение вещей: "ученик извлек из глубин своей бедной памяти давно забытую им информацию".

Nothing to add because I don’t argue English with non-natives. I’m a professional translator, linguist, editor and native English speaker. I stand by my initial corrections above. Instead of arguing, you should be learning))