He and the Osmonds used the same drummer, jumpsuit designer, Las Vegas hotel suite and shared an interest in religion.
When Elvis was away, the Osmonds stayed in his Hilton Hotel suite and when he was in town, he often sent them "bouquets in the shape of a guitar," Osmond says. "We talked on the phone and visited him. We were backstage with him."
Elvis was especially drawn to matriarch Olive Osmond, says LaVonne Gaw, an archivist/researcher at the Graceland Museum in Memphis -- a relationship Osmond confirms.
Elvis and Olive Osmond spent hours talking about Mormon principles, particularly the idea that families would be reunited in heaven, Gaw says. "He was close to his mother, who died when he was 23, and he was anxious to see her again."
Just to make sure, interested Latter-day Saints have traced Elvis' genealogy and had him baptized by proxy into the LDS Church -- numerous times.
"I think we've got a Brother Elvis up in heaven somewhere," Osmond says with a chuckle.
Indeed, Elvis was "my missionary," says Gaw, an LDS convert who became interested in Mormonism after hearing that Elvis read The Book of Mormon.
The Elvis-Mormon connection, so the story goes, may have begun in 1967 when the young Coulter found an apartment across the street from Graceland, Elvis' Memphis mansion. Every day, she stood at Graceland's gate hoping to catch a glimpse or a word from him. When he moved to L.A. to make movies, she moved, too, again becoming a familiar fixture hovering near his residence.
The superstar became comfortable enough to be on a first name basis with Coulter and allowed himself to be photographed with her -- photos she proudly displays in her home.
Coulter had been hanging around Elvis nearly a decade when she joined the LDS Church in 1976; her "inner peace" seemed to pique his curiosity, she says. So she shared her newfound faith with him, giving him a copy of the church's unique scripture.
The next day, Coulter says, he told her he was impressed with the book so she gave him several other Mormon works, including the Doctrine and Covenants. Then she called the LDS missionaries in Memphis and a pair visited the singer at his home -- something current LDS missionaries in Memphis are unable to substantiate.
"After the first discussion, Elvis knew more than the missionaries," Coulter says.
As part of the usual conversion process, the missionaries immediately challenged Elvis to be baptized.
"I'd like to but I'll be on tour," she says he told them. "If you wait until September, I'll do it."
A baptism date was set for the first Saturday in September, Coulter claims, but Elvis was dead by August.
Vernon Presley, Elvis' father, was apparently not pleased to learn of his son's interest in Mormonism.
Days after the funeral, Coulter says, Vernon Presley gave her back the scripture, which now included handwritten notations such as "I know this in my heart to be true."
By one passage, "Thou shalt have no other God before me," it says, "Not me either."
On the bottom of a page talking about the innocence of children were the words, "My daughter Lisa needs this church. She's nine. Please help her."
Coulter then donated the volume to the Graceland Museum, which eventually returned it to her.
Book in hand, Coulter made her way to Utah and crossed paths with the Osmonds, who expressed interest in it. So she loaned it to Alan Osmond, who showed it to family members and friends.
Finally the demand to see the book grew too large, Osmond says -- "all the LDS Elvis impersonators wanted it" -- so he gave it to the church. Before doing so, however, Osmond photocopied the pages.
"I held it for a long time, trying to find the right moment to give it to Lisa," he says. That opportunity came in the last few years when Lisa Marie Presley -- a Scientologist -- was on siblings Donny and Marie's talk show and the papers were given to her publicist.
Coulter was a bit miffed that Osmond gave the book to the LDS Church rather than back to her, but agrees that's the best place for her treasure. She is considering donating Elvis' Doctrine and Covenants to make a pair.
As to whether the notes in The Book of Mormon really were made by Elvis, no one can be sure.
"I made Cricket send a certified letter that it was true," says Osmond, adding, "I knew Elvis and those were clearly his words."
Gaw, who says the museum has another Book of Mormon believed to be Elvis' in its collection, echoes that sentiment. "His way of reading a book was to write in the margins."
The LDS Church archives has received many inquiries about the book, nearly one a week, Slaughter says. But neither the LDS Church nor the Graceland museum have tried to authenticate the handwriting.
Still, Coulter is sticking by her man, er, her story.
"I wish he had lived longer and joined the church -- it just didn't happen," she says. "I know he's up there doing his work like he's supposed to."
Picture this: Elvis' gyrating hips planted primly on a Mormon pew -- or the King of Rock 'n' Roll working as an LDS missionary in heaven, serenading the unsaved.
This vision is not too difficult for Cricket Coulter, an LDS convert who began her lifelong adoration of Elvis in the fifth grade. The fiftyish Coulter, who lives in Orem, claims that in the months before he died, Elvis was close to converting to Mormonism. She gave the "King" a copy of The Book of Mormon and Doctrine and Covenants.
Months after his death on Aug. 16, 1977, The Book of Mormon in which Elvis reportedly scribbled notes was returned to Coulter. Real or not, the writing in the blue paperback book has become yet another faith-promoting rumor circulated among Mormons with the same enthusiasm as speculation that actor Jimmy Stewart and filmmaker Walt Disney at one time looked into joining the church.
At least this legend has a paper trail.
Coulter loaned the book that supposedly bears Elvis' notations to Mormon entertainer Alan Osmond, who gave it to Ed Pinegar, an LDS general authority, who donated it to the LDS Church's historical department.
"We believe Elvis owned it, but we make no claims about the authenticity of the handwriting," says Bill Slaughter, an archivist for The Church of Jesus Christ of Latter-day Saints.
The inscribed Book of Mormon is not the singer's only link to Mormonism.
Elvis' karate instructor, the late Ed Parker, was a church member who discussed Mormon theology between kicks and chops and may have given him another Book of Mormon, according to associates of the King.
And Elvis felt a strong connection to the Osmond family, says Alan Osmond.