A DAUGHTER?
R E D H E R R I N G
In researching Mollie/Molly Law, I came across an Australian newspaper that contained a small sentence implying that she may have had a daughter. In the 'births' section of The Sydney Morning Herald, a daughter was born to a Mollie and Edgar, in New South Wales, with the surname Lawrence-Law. While this could be a complete coincidence, the names and location, make it something to look further into, especially since there is no mention of Edgar having a daughter, unless, she didn't live long after her birth.
The resolution of the newspaper is poor, meaning the text is hard to read, the missing portion below is likely the name of the hospital, possibly 'Royal [...]', I'll need to do more research before I can confidently say that this is, or is not, related to Edgar Law.