I don't think the 'Dear Boss' letter was written by the killer. As well, I doubt ANY of the correspondence received by police, Lusk, etc. was written by the killer.
Of course, we cannot know anything for certain at this point. This is simply my personal feeling. In my personal composite of the killer, he was just that: a killer. Everything else was extraneous, ancillary, even unncecessary. Killing was the thing. It was not a game. It was not something to be advertised or boasted about. It was his passion, compulsion, obsession. His focus was on what he was about, what he HAD to do. Therefore, I don't think he would have put pen to paper, contacted anyone, boasted, recorded in a diary or journal. Hoaxes all.
I believe he was a social imbecile. I believe he posessed some amount of intelligence that was not apparent due to his social awkwardness and strange personal manner. I also believe that witnesses who saw victims speaking and laughing with a man before their murders did not see the killer. I sense the killer was man of few words, very shy, someone his victims actually felt they had to draw out, or even for whom they may have felt some amount of pity. Shy. Awkward. Quite. Wouldn't hurt a fly. Until he cut their throats, that is. I believe the killer's name is foreign to us, unknown. He lived quietly, unnoticed. He died, silenly, mourned by few, missed by none.