Imagine 10 years from now someone in a Yale dining hall gazes up at a stained-glassed window with jagged graphic banderoles reading “Broken is Mended” and inquires: What in the world does that mean?

For more than 50 years, shards of colorful glass, preserved in 25 carefully labeled envelopes, had been stored in an old Italian shoe box under Fred McDonald’s bed. The broken bits, taken from bombed ...