In order to make them respect him, Major Warren shows them a personal letter that Lincoln have written to him. If a "white" powerful figure showed interest in him thus other white people will find him respectable. Lincoln was a major figure in the American history who wanted to create a strong unified country but was also known to be against the slavery system. That's why a letter from the president Lincoln adressed to a black man might have looked authentic. The last chapter of the movie named "Black Man, White Hell" makes it even more obvious. But the word "white" can have two significations : either the fact Major Warren is surrounded by "white" people and is about to die because he got shot by one of them or because all his misery happened
