LONDON — What does a billionaire philanthropist do when the art gallery he is sponsoring builds some pillars he doesn’t like? The answer, it turns out, is to have the last say from beyond the grave almost a quarter of a century later.

In the 1980s, British grocery store magnate Lord John Sainsbury, Baron of Preston Candover, spent tens of millions funding a new wing of London’s National Gallery. He did not like one aspect of the design, however: two nonstructural, false columns in the…