In his 2021 memoir, “Beautiful Things,” Hunter Biden took stock of his travails and wrote: “All my energy revolved around smoking drugs and making arrangements to buy drugs — feeding the beast.”

It is the type of admission that the government turned to in trying to use Mr. Biden’s own words to persuade a jury that he lied about his drug use.

Prosecutors say Mr. Biden misrepresented the extent of his drug use in completing a federal form to buy a firearm on Oct. 12, 2018. At the time, he replied “no” to the question: “Are you an unlawful user of, or addicted to, marijuana or any depressant, stimulant, narcotic drug, or any other controlled substance?”

Mr. Biden’s defense team argued that the terms “user” or “addict” are not defined on the form he filled out. They say the question itself is in the present tense.

“Someone, like Mr. Biden who had just completed an 11-day rehabilitation program and lived with a sober companion after that, could surely believe he was not a present tense user or addict,” Mr. Biden’s lawyers wrote in a court filing.

Yet, prosecutors say, Mr. Biden recognized he was an addict. They point to his memoir, in which he described in some length a four-year addiction to crack cocaine, a period that included his purchase of the gun. In detailing his multiple attempts at rehabilitation, Mr. Biden at one point concludes those efforts were “insincere.”

Recalling the tumultuous period of his life after he bought the gun, Mr. Biden wrote: “I hardly went anywhere now, except to buy. It was me and a crack pipe in a Super 8.”

In addition to excerpts from his book, prosecutors have singled out text messages and metadata retrieved from his phone days after he acquired the gun. On Oct. 13, Mr. Biden texted that he was meeting with his drug dealer, Mookie. The next day, he sent a message that read, “I was sleeping on a car smoking crack,” at an intersection in Wilmington.