Theory:

One of the Germans was waving a bottle above his head. “It is Christmas Day, Tommy. We have schnapps. We have sausage. We meet you? Yes?” By this time there were dozens of them walking towards us across no man’s land and not a rifle between them. Little Private Morris was the first up. “Come on, boys. What are we waiting for?” And then there was no stopping them. I was the officer. I should have stopped them there and then, I suppose, but the truth is that it never even occurred to me I should. All along their line and ours I could see men walking slowly towards one another, grey coats, khaki coats meeting in the middle. And I was one of them. I was part of this. In the middle of the war we were making peace.
 
You cannot imagine, dearest Connie, my feelings as I looked into the eyes of the Fritz officer, who approached me, hand outstretched. “Hans Wolf,” he said, gripping my hand warmly and holding it. “I am from Dusseldorf. I play the cello in the orchestra. Happy Christmas.”
 
“Captain Jim Macpherson,” I replied. “And a Happy Christmas to you too. I’m a school teacher from Dorset, in the west of England.”
Explanation:
  
Jim realized there was no trick. He saw one of the German soldier shaking a bottle above his head as if inviting them for a drink. He used the general name for British soldiers, Tommy. He invited the British saying he had schnapps and sausage and asked if they could meet. Schnapps is a German alcoholic drink made of grains. By this time, some soldiers started walking towards the common land, and there were no guns with them. Little Private Morris may be a name of the soldier, or may also refer to any British soldier in the war-front. Morris walked first and also asked the others to join him. Slowly groups of men started walking towards each other. Jim was the captain, the officer present there. He should have stopped such things like moving into the enemy side without rifles. But he confessed that it just did not occur to him, to stop them. All along the borders, he could see men moving in groups, the grey (Germans) and khaki (British) overcoats were mingling and meeting in the middle point in the common land. Jim felt he also indulged himself in this, instead of stopping this incident. He wrote they were making peace in the middle of a war. Jim felt so because they were there for war, but they were celebrating instead of  fighting.
  
He goes to explain to Connie - his feelings when he looked up into the eyes of the German (Fritz) officer. He extended his hand for a handshake and introduced himself as Hans Wolf. Jim noticed the warm grip of Wolf's hand in his, while he said that he was from Dusseldorf and he played cello in an orchestra. He wished Jim for Christmas.
  
Jim introduced himself, as Captain Jim Macpherson and he wished Wolf back for Christmas. Jim said he was a school teacher from Dorset, West England.
  
  
Meaning of difficult words:
  
Words
Meanings
Schnappsa German alcoholic drink made of grains.
sausageminced pork/meat dish
 
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.