I think there is a reasonable chance it could be passed on. There were two together west of Hamilton some years ago and others have been seen in and around Hamilton more recently, more than a tui lifespan later. I also saw one a couple of times in Pironga village over the summer.
The gene for the brown mutation is on the sex chromosome, so most birds with this condition are female, and indeed, all tui I have seen like this have been female.
Brown is the second most common colour aberration in birds (after progressive greying).
https://www.neilfitzgeraldphoto.co.nz/g ... ndiae_4762