Inheritance rights of nephews/nieces

I am British and am married to a Japanese woman. We have lived in the UK for over 30 years. My wife's natural father died when she was very young, but until recently 2 of his brothers wre still alive. One of her uncles died recently. He never married or had any children. He did own a house and the land on which it stands. Her other uncle is married, but has no children either. A legal firm in Japan has sent my wife a letter naming her as a "co-heir", but asking her to assign all rights to her uncle so that the estate can be sorted out quickly. From what I have read about Japanese inheritance law, only spouses, children, parents and siblings have any inheritance rights, so my wife would lose nothing by agreeing to the legal firm's request. She is on good terms with her uncle and does not want to upset this. At the moment we do not have any idea of the value of the estate. Am I correct in my interpretation of Japanese inheritance law?

I think she has an inheritance rights, as a substitute for her father.
The Civil Code of Japan consider as follows. Her father should inherit his brother, but he had died already. So, his daughter should inherit as a substitute.
(The Civil Code, 887th clause)
This is called Daishu-sozoku 代襲相続。