A letter from Arun to Uma would be able to discuss many of the novel's themes.
I think that a letter from Arun to Uma could focus on what it means to be an "outsider." Even though Arun is male and has the benefit of traveling abroad for his education, he experiences the plight of an outsider. Uma can understand this extremely well. She lives life as an outsider. She is not married, and has no prospects. She is overworked as she lives for her mother and father. She has had to live a life for other people. As a result, she understands the reality of marginalization and flight from people that Arun covets.
I think that a letter from Arun to his sister might begin with how it is possible to be alone in a crowd. Arun is surrounded by people in Massachusetts, but he is still alone. The letter could delve into his own psychological condition. He has not been able to trust people around him. Arun could write about how his life is one that has withered under the pressure from other people. Starting in India and continuing in America, Arun has never been able to find a place where comfort can be established. The letter could end with his desire to simply be away from people and social expectations, a reality that his sister could appreciate herself.