Funny I owned the same shares way back in the 80s and had to do something similar.
Your first port of call would be to do a thorough search through her papers Check for any other shares she bought and how she bought them as that might give you some clues. Bank Statements. Next her broker, Then registry services (Computershare, Link etc - who can be difficult to deal with especially with deceased estates, but you might get lucky)
Beyond that I'm thinking this probably has happened many times before and the ATO might have done a ruling on this.
