I think we may be making this more complicated than necessary. There are two questions.
First, does the museum own everything. If the will stipulates that everything goes to the museum and someone who has the authority at your museum has accepted it by signing a Receipt and Release form supplied by the executor, and the objects are at the museum, then you own it all.
You do need to look at the terms of the will. If there is nothing in it about having to keep everything, returning the money from anything you sell to the estate, etc., then you are free to do whatever you want with the objects. You can accession some, all or none.
The second question, the disposal of anything you don’t want to accession, is dependent on your own internal policies. It is not abandoned property, found in collections or anything else. It is all a gift.
The will itself serves as proof of your ownership (i.e., it is the equivalent of a Deed of Gift).
