This is an interesting question to consider, because in one sense, I think Jane is one of the few characters in this novel, apart from Phoebe of course, that Holden actually has the potential to connect with in a meaningful, non-phoney way. When he talks about her to the distracted Stradlater, it is clear that his friendship with Jane is actually tremendously important to him, and that they shared things at a very deep level. Holden talks about her interests and the kind of struggles she faced with her new step-father. The way that he keeps on talking about her, even when Stradlater pays him the courtesy of barely listening to him, indicates how important she is:
"Jane Gallagher. Jesus." I couldn't get her off my mind. I really couldn't. "I oughta go down and say hello to her at least."
If Holden were to write to Jane, therefore, I think he would perhaps feel free to write about some of the issues that are going on deep within him as a character, perhaps refering to his grief over Ally and the current disintegration he is experiencing. I wonder whether if he had been able to go down and speak to her whether the breakdown he experiences would have actually been avoided.