Donald Trump was notoriously averse to reading his briefing papers as president but according to Jared Kushner he has started reading Breaking History, his son-in-law and former adviser’s 500-page White House memoir.

Speaking to the Fox News host Brian Kilmeade on Wednesday, Kushner said: “When I gave it to him, he said, ‘Look, this is a very important book. I’m glad somebody wrote a book that’s really going to talk about what actually happened in the room.’ And he says, ‘I’m going to read it.’

“So he started reading and he’s given me some compliments on it so far. And again, I hope he’s proud of it. I don’t know if he’ll like anything [in it].”

Critics have not liked much in Kushner’s book. For the Guardian, Lloyd Green called it “a mixture of news and cringe” which “selectively parcels out dirt”. In the New York Times, Dwight Garner called the book “earnest and soulless”, saying “Kushner looks like a mannequin, and he writes like one”.

“Kushner’s fealty to Trump remains absolute. Reading this book reminded me of watching a cat lick a dog’s eye-goo,” Garner wrote.

Kushner has said he “read that review and … thought it was hysterical” and wanted “to hang it on my wall”. He also said sales had increased since the Times piece. The book does not appear on the Times bestseller list.

Married to Trump’s oldest daughter, Ivanka, Kushner was a senior adviser through a presidency that ended in a deadly attack on Congress as Trump attempted to stay in power.

Kushner said: “Sometimes he listened. Sometimes he didn’t but we had a lot of fun.”

Whether Trump will finish Kushner’s book remains to be seen. The former president has never been known to be much of a reader – although his first wife, Ivana Trump, did say he kept a volume of Hitler’s speeches by his bed.

At the time, Trump told Vanity Fair: “If I had these speeches, and I am not saying that I do, I would never read them.”