The detailed reports of Mr. Abdulmutallab may also play into the debate President Trump has renewed about whether torture is ever necessary to get useful information from terrorism suspects. Most experienced interrogators say no, and their arguments would receive support from these interviews.

Image Mr. Abdulmutallab tried to carry out the attack but failed to detonate explosives hidden in his underwear. Credit... Reuters

The F.B.I. flew Mr. Abdulmutallab’s relatives to the United States to boost his spirits and encourage him to talk — with great success. In interview after interview, he described every person he said he could recall from Al Qaeda in the Arabian Peninsula, the branch in Yemen; discussed candidly his evolving views about carrying out a terrorist act; and tried to reconstruct the layout of a training camp, Mr. Awlaki’s house and many other Qaeda buildings. His descriptions were so precise that it is likely they have helped shape targeting decisions in the American drone campaign in Yemen.

Mr. Awlaki, whom everyone at the Qaeda training camp called “sheikh” out of respect for him as a religious leader, spoke at length with the Nigerian, then 23 and the son of a wealthy banker, about what he saw as the religious obligation of jihad. He put the younger man up at his house in the province of Shabwah, where Al Qaeda had a large presence, and introduced him to other Qaeda trainers and bomb makers, Mr. Abdulmutallab told the F.B.I.

Mr. Awlaki helped Mr. Abdulmutallab prepare a martyrdom video, telling him to “keep it short and reference the Quran.” He gave the recruit a way of staying in touch, evidently an email address, to report on the proceedings.