The Kurds’ commander, Mazlum Abdi, said on Monday that they had helped confirm Mr. al-Baghdadi’s identity by stealing his underwear and obtaining a blood sample, both for DNA testing.

The U.S. joined forces with Mr. Abdi’s group five years ago. Our reporters reconstructed how that partnership fell apart after President Trump withdrew American troops from Syria.

Watch: Mass funerals, wounded children, displaced families. Our video documents what our journalists found in northeastern Syria.

Reaction: Those who suffered under the Islamic State greeted the news of Mr. al-Baghdadi’s death with grim satisfaction at best. “He deserves a worse and more abhorrent death,” said one man in Mosul, Iraq.

Another angle: Mr. Trump shared a photo of a dog that participated in the raid, saying its name remained classified. Gen. Mark Milley, chairman of the Joint Chiefs of Staff, said the dog “is still in theater, returned to duty.”

The Daily: Today’s episode is about Mr. al-Baghdadi.