Theory:

The time came, and all too soon, when the game was finished, the schnapps and the rum and the sausage  had long since run out, and we knew it was all over. I wished Hans well and told him I hoped he would see his family again soon, that the fighting would end and  we could all go home.

 “I think that is what every soldier wants, on both sides,” Hans Wolf said. “Take care, Jim Macpherson. I shall never forget this moment, nor you.” He saluted and walked away from me slowly, unwillingly, I felt. He turned to wave just once and then became one of the hundreds of grey-coated men drifting back towards their trenches.

That night, back in our dugouts, we heard them singing a carol, and singing it quite beautifully. It was Stille Nacht, Silent Night. Our boys gave them a rousing chorus of While Shepherds Watched. We exchanged carols for a while and then we all fell silent. We had had our time of peace and goodwill, a time I will treasure as long as I live.

Dearest Connie, by Christmas time next year, this war will be nothing but a distant and terrible memory. I know from all that happened today how much both armies long for peace. We shall be together again soon, I’m sure of it.

Your loving, Jim.
Explanation:
 
The match ended, the food and drinks also ended. They came to the end of the Christmas celebration. Jim wished Wolf well and told him that he hoped to see his family some time and that the fight would end soon so they all can go back to their families.
  
Wolf replied saying that's what every soldier would want, on both sides. He told Jim to take care of himself and that both of them will never forget the moments they had shared. He saluted and walked away from Jim. Jim felt he hesitated to walk away from him. Wolf turned one last time to wave goodbye and mingled as one amongst his troops. All his men were going back to their trenches.
 
The soldiers slept in the space made by digging a hole in the ground and covering it with a roof. These holes are called dugouts. That night when they went back to their dugouts, Jim's troop heard Wolf's troop singing carols beautifully. They had sung Stille Nacht, or Silent Night in English - a popular Christmas carol. Jim's men sang the carol "While Shepherds Watched Their Flocks" and made them feel emotional, excited, and enthusiastic. They all had a peaceful and benevolent time that day. Jim said he would treasure the memories of this time for as long as he lives.
 
Jim ended his letter saying by next Christmas, and this war will only be a distant and bad memory. He wanted the war to end as soon as possible, and he felt that was the longing of both the armies. He signed off saying he's sure that they will be together soon.
 
 
Meaning of difficult words:
  
Words
Meanings
DugoutsA trench that is dug and roofed over as a shelter for troops.
Rousing chorusMaking you feel emotional, excited, or enthusiastic.
 
Reference:
National Council of Educational Research and Training (2008). Honeydew. The best Christmas present in the world - Michael Morpurgo (pp. 9-16). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.