Once you use the mine cart to sneak past the gunner position and dig down into the trench tunnel, go through the door on your right and find this item on the floor next to some barrels.
"21 April 1915
We've been stuck down this hole since January, and I can't stand it any more. I'm sick to the back teeth with living like a rat. I really miss life as it was before, strolling beneath the linden trees with you. I even miss working in the factory.
All my love,