From Wikipedia:
Harry, its English short form, was considered the "spoken form" of Henry in medieval England. Most English kings named Henry were called Harry. The name became so popular in England that the phrase "Tom, Dick, and Harry" began to be used to refer to men in general.
And as the interment for William Henry in grave number 32473 was carried out in 1958 at the age of 67, then the conclusion must surely be that he was known as Harry, and the husband of Emily, and that the inscription refers to him, rather than the son.