Wills, probate, letters of administration, powers of attorney
I would have thought that without a will the executor would be the Public Trustee. Once they gain probate they will be allowed to administer the estate and then shouldn't have an issue with recoving the funds from the investment company. (All they need to show the investment company is proof of probate.)
Also note the bank may also make payment of the funeral expenses out of the deceased estate without intervention from the executor (and before probate is granted) - I'm not sure if all banks do this though.