A note, knowing his fingerprints would be on it plus writing to compare with various other notes found at WHF ? He may as well have written another note to EP telling them it was him because they had no other proof.
Why do his fingerprints need to be on any other notes? There's the one which looks as if it's been written by children practicing their letters, and the note which is probably June's aide de memoire for a bible class. Despite it being hinted at broadly, there's no proof of any other note.
There is, however something claimed to have been Sheila's suicide note, but as it appeared, here on the forum, it could just as easily have been another of the many fake exhibits which have, mysteriously, found their way here, even before the authorities get a sniff of them.