Sell shares of deceased person as the POA of deceased person's partner

On behalf of a loved one (I'll monitor and respond if necessary):

About 10 years ago, my Dad passed away without a will. I would like information on transferring his small number of shares into my Mum's name. I avoided this earlier because dividends are still being paid into his account, which I can access as an authorised person (though I haven’t made any transactions). I’m my mother’s caregiver and Power of Attorney (POA).

I have my father’s death certificate and access to my mother’s bank account. I have no idea of who his shares are registered with. When my father was alive, I was his administrator under QCAT, but I no longer have that documentation. Could a process be suggested to transfer the shares into my mother’s name so I can close the account and move everything into her name?