What does the sniper do to trick his enemy in the short story, "The Sniper"?

The sniper was on a rooftop.  He lit up a cigarette, and the glow of the cigarette gave away his position.  A bullet hit the wall of the roof near where he was sitting.  An enemy soldier was aiming at him from across the street. He tried to locate the enemy’s position but could see nothing.

Just then, an armored enemy car drove down the street and met an old woman, who pointed out the...

The sniper was on a rooftop.  He lit up a cigarette, and the glow of the cigarette gave away his position.  A bullet hit the wall of the roof near where he was sitting.  An enemy soldier was aiming at him from across the street. He tried to locate the enemy’s position but could see nothing.

Just then, an armored enemy car drove down the street and met an old woman, who pointed out the sniper’s position.  He fired and killed the machine gunner in the car, and then fired again and killed the woman.  In order to do that, he had to give away his position, and the enemy on the roof across the street fired again, wounding  the sniper in his arm.  His forearm was dead to any feeling.  He couldn’t lift his rifle any longer. 

The sniper knew that he needed to kill the enemy, or he would never get off the roof.  But first he had to locate him.  He took off his cap, placed it on the muzzle of the rifle, and lifted the rifle until the cap was over the parapet of the roof.  Immediately a bullet pierced the cap.  The enemy, thinking the sniper was dead, stood up.  When he did that, the sniper was able to shoot him using his revolver. The dying man fell forward, fell off the roof, and hit the ground, dead.  Later the sniper would discover that the enemy was his own brother.