The poem was called “The Greatest” and when Joe Pappalardo handed it to Muhammad Ali — by then, suffering from Parkinson’s disease — Ali began to weep.

“It was amazing,” said Pappalardo, 68, whose halting speech is due to cerebral palsy but is at no loss for words when he speaks of the days Ali descended on Roosevelt’s cerebral palsy association in June 1996. “I didn’t expect him to cry when I gave him the poem, but he was very sensitive.”

Ali died late last Friday at the age of 74, and there has been talk of his mighty achievements in the ring, his fight for civil rights, his controversies and, of course, his legacy. But for the people of Cerebral Palsy of Nassau County — participants as well as teachers, nurses and administrators — Ali’s legacy can be encapsulated by those 2 ½ days he spent on Long Island. He visited every single member, giving out autographs and hugs long after his handlers had advised him to rest, his Parkinson’s sapping his strength.

Monday afternoon, many of them gathered, and with them, they brought the pictures they took with the champ, along with the memories that made Ali’s visit a watershed moment for the center, a nonprofit that offers a number of health and recreational services, and has been open since 1948. Nearly every person mentioned Ali’s warmth.

“He lay down with each person that was on a mat table,” said executive director Bob McGuire, referencing the tables used for those using wheelchairs. “He shook everybody’s hand, physically touched each of our adult participants . . . It was remarkable.”

It all happened because of a friendly conversation over dinner. Tony Galano, vice president of the board of directors, had dinner plans with a friend who happened to know Ali and brought him along. Galano told Ali about the center, and how they were planning to have a sports memorabilia fundraiser, and would Ali like to come?

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“And he said sure. He said it so fast,” Galano said.

What resulted was more than just a few handshakes and pictures at a fundraiser. Ali came for the cocktail party, a corporate breakfast, a dinner, and another breakfast. The center sold every piece of memorabilia it had to offer, Galano said. But that’s not what he remembers the most.

“At breakfast, I looked around and saw that all the directors and supervisors had tears in their eyes,” he said. “And I look, and I see Muhammad had bent down to hug the kids that couldn’t get up. He’s hugging them and kissing them, and then there was one little boy that couldn’t really speak, and the boy saw him and said, ‘Muh-hammad.’ And I say, ‘How did he know?’ ”

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The stories come quickly, and though a number of people who met him that day can no longer speak, they find a way to share what meeting Ali meant to them.

“He got happy to see us and his face was really smiling,” wrote Tricia Pikul, 43, on a device meant to communicate for her. “I like nice people and he was a very nice person,” wrote Robin Newsome, 49.

McGuire recalled how they had been told not to ask for autographs, but that Ali “was giving them out left and right.” He gave McGuire’s wife, Isabelle, about five drafts, because he didn’t like how the Parkinson’s would cramp his writing.

“To me, it was almost like seeing an old friend,” said Christine Arnone, 47, one of the participants. “I remember him walking through my classroom, hugging everybody and shaking everybody’s hand and his warmth and uniqueness definitely came through.”

Maura Wachsberger, 63, a teacher at the center, remembered that Ali would carry a rag to wipe his mouth, and how so many there had to do the same. “I think a lot of our guys could relate to that and he could relate to our guys,” she said. “It was a mutual admiration. You don’t see it every day. He was very special.”

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Bob Lares, 67, and Howie Cohen, 56, who both struggle to speak because of their disorder, soldiered through when it came to talking about Ali. “Everyone called him the champ and he loved it,” Lares said. “And then he shook my hand and I’ll never forget that.”

Cohen had difficulty saying the word he wanted, so he spelled it: “Awe.”

“I was in awe,” he said. Cohen called Ali “one of my heroes . . . I looked up to him.”

And Ali didn’t miss anyone. He made it to the cafeteria, where Carolyn Redd, 54, also a participant, said he “hugged and kissed me.” Lidia Ortiz, a nurse, was in the last room of the center. “I said he wasn’t coming,” she said, “and there he was.”

Martin Gagliano, 59, has a picture of him and Ali, and they’re mid-embrace. He lights up when he talks about that day, mouth splitting in a grin that threatens to take up his entire face.

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“My memory, beautiful,” he said, grasping at his heart and rubbing it when he thinks his words may not be understood. “Happy.”