In an interview with Rolling Stone, Jackson has alleged Depp and Beck have not credited lyrics belonging to Wilson.
Jackson met Wilson in 1964 while in Missouri State Penitentiary in the US. Jackson went on to publish a book in 1974 in which he documented much of Wilson's poetry, including the piece in question.
Wilson later turned the poem into a song called Hobo Ben, which is alleged to have been used by Depp and Beck in a song on their album 18.
Speaking to Rolling Stone, Jackson said the song extensively pulls lyrics from Hobo Ben. He said Depp and Beck have only contributed two lines. “Everything else is from Slim’s performance in my book," he said.
"I’ve never encountered anything like this. I’ve been publishing stuff for 50 years, and this is the first time anybody has just ripped something off and put his own name on it."
Depp and Beck are the only writers credited on the song and there has been no acknowledgement from the pair about Hobo Ben.
Jackson’s son Michael, who is a lawyer specialising in music and intellectual property rights, also told Rolling Stone the credits “do not reflect the actual authorship of those lyrics”.
“It’s just not plausible, in my opinion, that Johnny Depp or anybody else could have sat down and crafted those lyrics without almost wholly taking them from some version of my father’s recording and/or book where they appeared," he said.
Neither Depp nor Beck have made a statement regarding the allegations.
Wilson served time in jail for murder and robbery in the 1960s.
The album 18 has 13 tracks on it and was released last month. It mainly features cover songs. There are renditions of Marvin Gaye's What's Going On, John Lennon's Isolation and, controversially given its subject matter covering sexual violence, the Velvet Underground classic Venus in Furs.
A defamation ruling in June awarded Depp $10 million in damages and his ex-wife Amber Heard $2m. However, the bitter fight between them is continuing as Heard has launched a number of court appeals.
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