Dennis Haley has dedicated his life to proving that Riebe killed at least six women, aged between 15 and 35, while he serves a sentence for just one murder.
He reportedly confessed to several more murders to friends, family and even one of the victim's grieving father, but later retracted them.
Although he still denies the crimes, Morgan, 52, set about getting the truth, which resulted in Riebe storming out of the interview.
No one knows the exact motive for the crime, but the Good Morning Britain presenter explained to ITV viewers today that he had "flashes of anger" and it is that that the police believe was the cause of him snatching "vulnerable" women.
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Haley furthered the explanation, adding that Riebe was obsessed with one of America's most notorious serial killers, Ted Bundy, who was executed in 1986 for the murder of 35 women.
The detective said: "He was fascinated by Ted Bundy and I think he fancied himself being another one.
"I don't know if that was his motivation exactly though."
Haley added that he is still searching for corroborating evidence to pin the murders on Riebe, adding that he is certain he was behind the murders.
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"He revealed deals that only the killer could have known," he said. "The murder of Jacqui Brandt we didn't even know it was a murder and then he describes things that were never printed in a paper because it was never printed as homocide."
Morgan was keen to thank Haley for his tireless efforts to get closure for the victims' families, praising: "Dennis is an amazing guy because he never let go. We must thank him."
Riebe's full interview can be seen on ITV tomorrow at 9pm.