If he had a brother and they were close, presumably he would write (if he hadn't before) about his plan to leave Mary. I would imagine that he would want to tell his brother why he was leaving Mary and what he planned to do.
When I read this, I try to think why Patrick has decided to leave Mary. I imagine that maybe he has met some other woman who is more exciting than Mary. I imagine that he has gotten bored because Mary is so passive and such a perfect wife. I picture him having met someone who is more passionate and temperamental.
So I would think that Patrick would write to his brother about that -- about how his life with Mary has gotten dull and predictable and he wants to share excitement with this other woman.
Why do you think he was going to leave Mary?
Very interesting idea! Of course, what goes to the heart of this question is what Dahl is very careful not to reveal: the reason why Patrick is going to leave Mary. We as readers are left to guess at the reason, but I think there are definite clues in the text that point at guilt on Patrick's part. Note the following description:
He had now become absolutely motionless, and he kept his head down so that the light from the lamp beside him fell across the upper part of his face, leaving the chin and mouth in shadow. she noticed there was a little muscle moving near the corner of his left eye.
The nervous tic mentioned and the way he is keeping his face partially in shadow indicates that he is very guilty about what he is about to do and wants to hide himself as he tells Mary that he is going to leave her.
I think therefore that if he were to write a letter to his brother that morning, it would explain his decision to leave Mary and give the reason why. The most likely guess to my mind is that he has met another woman who is more exciting and interesting than Mary. Perhaps Patrick got tired of how obsessed Mary was with him - she certainly is described as being the model of a loving and an affectionate wife, which is perhaps what Patrick did not want. We can only guess, but his letter would, I think, express his feelings of guilt at leaving Mary.