Succession of Administration If Executor of Will Dies?

As a general rule, if an administrator dies intestate, there has to be a new application for new Letters.

https://www.lawsociety.com.au/resources/areasoflaw/ElderLaw/WillsestatesFAQs/index.htm

Hello Tim,

What happens when an administrator passes away with a will (deceased estate 2), but they were in the process of administering a deceased estate that was intestate before they died (deceased estate 1)?
Does the executor of the recently deceased administrator need to apply for a new LOA grant to administer deceased estate 1?

Example:
Jenny is the administrator for her sister Paula's intestate deceased estate.
Jenny passes away 12 months after the LOA is granted and Paula's estate has not yet been distributed.
Jenny has a will, naming her daughter Amy as executor.
Amy takes probate for Jenny's estate.

Does Amy need to apply for a new grant of LOA to administer Paula's estate?
Or as the trustee for Jenny, does she automatically become the trustee and the legal personal representative for Paula's estate and thereby entitled to distribute Paula's estate assets on this basis?

What is the difference in duties, responsibilities and powers, between an administrator of a deceased estate, a trustee of a deceased estate and a legal personal representative of the deceased?

This is all in Victoria.

Thanks for your reply!