The last time Ms. Shaw and Ms. Warner took on one of his plays — “Foot Falls” in 1994 — there was a showdown with the estate over a few altered stage directions that led to a firestorm of controversy and a circus in the British press. It didn’t end amicably. She was “banned for life” by the estate, Ms. Warner said in her deep and dry British accent, “which is extraordinary when you think: ‘Here I am.’”

This time Ms. Warner and Ms. Shaw adopted a diplomatic strategy, establishing an early and open dialogue with Edward Beckett, the playwright’s nephew and executor of his estate. He was very receptive to the idea of Ms. Warner’s directing, although her first idea — a new version of “Waiting for Godot” starring Ms. Shaw and Maggie Smith — was nixed. Ms. Warner returned to the estate with the idea of “Happy Days” (suggested by Nicholas Hytner, director of the National Theater), explaining that they planned a faithful production with a few small changes, like transforming the set from a small mound to a vast, post-apocalyptic landscape that looks like the charred remains of an environmental disaster.

Edward Beckett, who has seen the show in London twice, had no complaints. Even though Ms. Warner inserted the theme song to the sitcom “Happy Days” during intermission as a joke, she paid special attention to the wishes of the playwright.

“I’ve never seen Deborah standing there with a music stand, checking on the stage directions,” Ms. Shaw said. “Usually she’s watching, waiting for something to happen. That was radically different.”