The internal conflict that the sniper faces takes place at the end of the story where he has to wrestle with whether his actions have meaning.
Throughout the story, the sniper is committed to his mission. Taking out the target, his role in the machinery of war, and having the focus with which he commits himself show conviction. He does not experience much in way of internal conflict until he accomplishes his mission by killing the opposing sniper.
When the sniper has fulfilled his assignment he must confront the consequences of his actions. At this moment, the sniper experiences emotional struggle. The "lust of battle" departs from him when he sees the dead body of his adversary. The sniper wonders whether what he has done is worth it, struggling to find purpose in his actions. A hollowness emerges from the recognition that he has killed a fellow soldier.
It is at this point that the young person in the sniper is presents itself. Like many young people immersed in war, there is a conflict between its harsh realities and the innocent hopes of averting it. The sniper experiences subjective strife because of this collision. He cannot find solace in his action. He can only look at what the death he has caused. He struggles with this "cursing the war, cursing himself, cursing everybody" as a result. The accomplishment of his mission and the questioning of its purpose is when the sniper experiences internal conflict.