President Biden said at a wildfire-focused event in Idaho Monday that his “first job offer” came from the local lumber and wood-products business Boise Cascade, but the company says it has “no record” of that being true.

Biden, who is renowned for sharing memories that did not happen, said that he regularly mentioned the job offer to his Senate colleague from Idaho, the late Democratic Sen. Frank Church.

“I used to tell Frank Church this, I got a — my first job offer, where I wanted — my wife, deceased wife and I wanted to move to Idaho because we — not a joke — it’s such a beautiful, beautiful state. And I interviewed for a job at Boise Cascade,” Biden said.

He added: “And in the meantime there was a war going on. Anyway. But the whole point was that I used to always kid Frank.”

But Boise Cascade spokeswoman Lisa Tschampl told The Post, “We have no record of President Biden’s application or of him having worked for the company. “

Tschampl said that “we checked our system internally and nothing has turned up.”

The White House did not immediately respond to a request for comment.

The Post was unable to locate any prior record of Biden mentioning the company — including in news clippings archived by the Nexis and Factiva databases.

Biden’s 2007 memoir “Promises to Keep” does not mention the company or a desire to move to Idaho.

It’s unclear where the Idaho application would fit in the president’s Delaware-centric legal and political career.

Biden graduated from Syracuse University’s law school in 1968 and received a medical draft deferment from the ongoing Vietnam War due to a history of asthma. He then worked as a law clerk and public defender in Delaware before he joined the New Castle County Council in 1970.

His autobiography says Biden and his late wife, Neilia, whom he married in 1966 while in law school, moved to his home state of Delaware in 1968 shortly after he earned his law degree.

Biden wrote that during his final year in law school, “Neilia and I still hadn’t settled on where we were going to live, so I hadn’t accepted a job.” But his father in Wilmington, Del., set him up for a meeting with a local judge, who referred him to a lawyer, whose firm offered him work.

In 1972, Biden was elected to the US Senate. His first wife died in a car crash shortly after his Senate election victory.

Tschampl, the corporate spokeswoman, allowed that it’s possible Biden did seek employment with the company but that records were lost when the company dropped some of its past projects, such as concrete, plastics and textile divisions.

Biden has a record of inaccurate or embellished claims. He dropped out of his first presidential campaign in 1988 due to a scandal involving plagiarism of speeches and a law school paper and controversy about claims he made about his academic record.

But as the nation’s oldest-ever president, Biden’s mental acuity also is a frequent matter of public debate.

Biden this month falsely claimed that he remembered “spending time at” and “going to” the Tree of Life synagogue in Pittsburgh after the October 2018 mass murder of 11 people. After the synagogue said that he did not visit, the White House said he misspoke and was referring to a 2019 phone call with the congregation’s rabbi.

In one infamous misstatement, Biden in 2020 claimed he “had the great honor of being arrested” in South Africa when he was “trying to get to see [Nelson Mandela] on Robbens Island,” where Mandela was in prison until 1990. He said Mandela thanked him for it. Later, he admitted that it was untrue.