I'll have to find these original custody documents. I believe she went under the name Moore when she could but ultimately used Fullbrook in all her documents into the future. It's not very clear what happened with William after that. Apparently he died 16 Nov Tennyson, Napier, New Zealand.
On a side note. I googled the named
Gordon John Heath, who seemed to have married Agnes' great granddaughter Merle Mary Fullbrook. Apparently he died in 2011. So I looked up the white pages for Heaths in that area and there weren't many. The first one I rang turned out to be Merle, still alive in her 80's

Instant way to make a new relative. So that was a nice chat. I can send her photos of Agnes and Agnes Ann now and hopefully she'll send what she has soon.
Fortunately I'd done research on William Wood Fullbrook before I realized he wasn't my relative, so now someone can still benefit. Much of what I learned about Agnes is through this Forum too. So the whole family is benefiting so much. Thanking everyone again!