As a fit-for-combat soldier stationed in the buffer zone, sergeant Kovalev would regularly escort IDF personnel moving within the zone. On October 24st, 1998, he escorted base commander colonel Haim Katz to an ex-phalangistes family in Bintj Beil. Givati sergeant David Shabanov, who took part in the armed convoy, recalls:

"Influent lebanese families were used to invite our base commander around a well-dressed table. Sometimes we were allowed to take turns at the table, but most of the time we were waiting outside next to the GMC while they’d eat and discuss inside. Still, it was customary that members of the hosting family would bring us food. On that day, we were waiting outside the newly-built villa of the Jebayel family when a girl in an elaborately embroidered dress - at most sixteen years old - came outside with a plate and offered it to each of us. When she faced sergeant Kovalev, I noticed something strange in her behavior. She talked to him very fast, and she kept repeating, ’I know who you are...’. I saw sergeant Kovalev whisper something into her ear, and then she walked away silently. I asked him what it was all about, but he just nodded with his shoulders and said nothing."

Overt anti-IDF conduct was clearly evidenced once. Major sergeant Shlomo Katzen reports an incident during the escort of a suspected hizbollah collaborator that had to be transferred from the hospital in Marjayoun to detention center Al-K’hiam . Sergeant Kovalev was quoted to have said, "IDF occupies the territory, Shin Beth punishes it."

"A Shin-Beth officer who had heard what he had said started to insult him. Although sergeant Kovalev didn’t respond verbally to the insults, he gave him a defiant and angered look. We pulled him away before it turned nasty."

Soldier Yossi Erez was Abraham Kovalev’s closest friend. Transcript of his interview reads as follows:

"Marjayoun is packed with officers. In all the bases I’d known before, low grade soldiers were the bunch, officers the happy few. Here it’s the opposite. Except for combat units securing the outpost, who’d shift every three months anyway, the vast majority of the personnel is high-graded, and totally oblivious to simple soldiers. I think this is the reason why Sergeant Kovalev offered me his friendship. We both knew we’d probably never see each other after those three months. We met under special circumstances. My company and I had just arrived to Marjayoun. We were called to participate in a special operation. We took position in a ruined building on a hill, two kilometers away from an enemy position. It was not an ambush, but an artillery mission. We were mere reinforcements. We had a long night before us, shelling would not start before dawn. At one point I noticed a light beam through a hole as big as a wall in the devastated building. It was sergeant Kovalev reading a book with a flashlight. I asked him what he was reading. Stories, he said. I said, well why don’t you tell me one. He told me the story of a shaman who devoted his life to fabrication. In particular, he wanted to create a real man with the power of dreams. The shaman succeeds so well in his efforts that he becomes that man, but before dying, he realizes he was just another sorcerer’s dream. That was typical of him. He often insisted on how the mind was a powerful and dangerous thing to play with. We went on talking about dreams and stuff, fantasizing about the possibility of monitoring mental activity so as to dream away our military service, but then authorization for shelling was signaled, and the place got filled with the drilling noise of mortars being shot out of the position. In the distance we heard machinegun and rifle fire being returned at us. They sounded like firecrackers. "Life is a dream", he said when the operation was finished. These were actually his grandmother’s last words, a down-to-earth woman who lived and died in Moscow. He told me he always had them in mind and I believe that.