month of a person's death
Used in Buddhist memorial contexts to refer to the month in which someone passed away. Often appears in phrases like 祥月命日 (しょうつきめいにち, the anniversary of the death).
Next month is the month of my father's death.
祥月命日にはお墓参りに行きます。
On the anniversary of the death, we visit the grave.
anniversary of a person's death
Here 祥 denotes a death-anniversary observance, as in 祥忌; 祥月 is the month containing the anniversary of a person’s death.