Joint Security Area

Two North Korean soldiers are killed in the DMZ at a North Korean border house, before Sergeant Lee Soo-hyeok (Lee Byung-hun), a South Korean soldier on border duties, attempts to flee back to the South Korean side. The southern troops rescue him while the gunfire erupts and, two days later, the fragile relationship between the two Koreas depends on a special investigation conducted by Swiss Army Major Sophie E. Jean (Lee Young-ae) on behalf of the Neutral Nations Supervisory Commission.
As Sergeant Lee Soo-hyeok has confessed to the shootings, Sophie investigates why the two Koreas have contradicting accounts of events; Soo-hyeok's states he was knocked out and kidnapped while relieving himself and, waking tied up in the North Korean border house, secretly freed himself and shot three North Korean soldiers, leaving two dead. The North Korean survivor Sergeant Oh Kyeong-pil (Song Kang-ho) states that Soo-hyeok barged into the border house and shot everyone before retreating when the wounded Kyeong-pil returned fire.
The autopsy report shows that one soldier, Jeong Woo-jin (Shin Ha-kyun), was shot eight times repeatedly, indicating a grudge was held; additionally, a single bullet is not accounted for. Over the course of the investigation, witness Private First Class Nam Sung-shik (Kim Tae-woo) attempts suicide by jumping out of the window of the interrogation room and a strange emotional reaction between Kyeong-pil and Soo-hyeok during a meeting causes Sophie to confirm her suspicions that the surviving soldiers and Woo-jin held a mutual friendship and were attempting to protect one another.
Explained through flashbacks it is shown that Soo-hyeok was on patrol with other soldiers, only to get lost on the North Korean side and to partially trip a mine; found by Kyeong-pil and Woo-jin, the two deactivate the mine, which later prompts Soo-hyeok to throw written messages over the border to maintain contact. Eventually inviting Soo-hyeok across the border, the three become a group of friends that soon includes Sung-shik, with the four agreeing to leave politics out of their friendship so to remain loyal to their own country.
As tensions rise between the North and South, Soo-hyeok and Sung-shik return to the North to say goodbye and celebrate Woo-jin's birthday, only to be discovered by a commanding officer from the North and resulting in a Mexican Standoff. Despite Woo-jin panicking and betraying his friends, Kyeong-pil convinces Woo-jin, Soo-hyeok and the officer to lower their weapons, only for Sung-shik to panic and shoot the commanding officer when he reaches for his radio; when Woo-jin draws his gun again, Sung-shik shoots him, and in a daze shoots his corpse several times. Earlier in their friendship when Soo-hyeok is joking around with his gun, Kyeong-pil asked Soo-hyeok if he'd ever had to kill a man like he's had to, implying that Soo-hyeok doesn't know what it's like. Kyeong-pil slaps Sung-shik out of his daze, takes the gun from him and kills the still-alive officer, then persuades Soo-hyeok and Sung-shik to flee with a false alibi of being kidnapped, before throwing away the evidence that he and Woo-jin were fraternizing with Southern soldiers. After shooting Kyeong-pil in the shoulder to complete the alibi, Soo-hyeok and Sung-shik flee across the border, with the latter getting past unseen; as Soo-hyeok's wounded leg from the firefight prevents him from running, he is the only soldier seen and picked up by soldiers.
Sophie is eventually removed from the case when it's discovered that her father, a former POW, had North Korean ties during the Korean War, thus technically making her a non-neutral. Before leaving, she attempts to informally learn of the true events first with Kyeong-pil and then Soo-hyeok. Having asked Kyeong-pil if he had a message for Soo-hyeok, Sophie gives Soo-hyeok the lighter he first gave to Kyeong-pil. Before saying goodbye and wishing him well, she reveals that Kyeong-pil told her that he saw Soo-hyeok's gun actually shot Woo-jin first during the chaos before Sung-shik shot him. On his way out, Soo-hyeok steals an officer's pistol and commits suicide out of guilt for Woo-jin's death and Sung-shik's suicide attempt. The film concludes with an American tourist's photograph of the joint security area that accidentally contains all four soldiers prior to the incident.

Question: What does Sophie give to Soo-hyeok?
Answer: The lighter