For example I want to write "Professor Neville died, but I am going to ask his wife Virginia Neville, who is acting as is _____, to forward you his confidential letter of reference that he wrote for me before before he died".
The exact title of the person who officially “takes over” for someone after they die depends on how they become responsible for this task:
If the deceased has left a will and named a person to act on behalf of the estate, then this person is the executor ;
if the deceased has died intestate, and a person has been appointed by court to administer the estate, then this person is the administrator of the estate.
A common term that may be used for both types is legal personal representative - however, there are also other types of personal representatives, e.g. a legal guardian.
Note that this may vary by jurisdiction. These terms are generally used in common law jurisdictions.
With all that said, I don't think you need the official title - at least not in the given example, where in most likelihood you would not even know what that title is, nor would the recipient care. You could simply write:
Professor Neville died, but I am going to ask his widow Virginia Neville to forward you his confidential letter of reference that he wrote for me before he died.