At Gabriel Kovari's inquest in June 2015, police were asked if there could be a connection to the death of Anthony Walgate the year before. A detective said there was "no link apparent".
Port went on to murder his fourth victim in September that year.
Coroner Nadia Persaud recorded an open verdict at Mr Kovari's inquest, saying there was no "reliable evidence" on which to base her findings.
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Transcripts of Mr Kovari's inquest obtained by the BBC reveal that his former flatmate, John Pape, raised concerns about a possible link between the death of his friend and that of Mr Walgate.
A detective who gave evidence at the inquest was asked by Mr Pape about the "unexplained death, quite close to the cemetery".
He added: "Was it even considered that there could be any link with that?"
Det Insp Rolf Schamberger replied: "I wasn't involved in that investigation, but I'm aware that an incident took place nearby not long beforehand, and that there was consideration given to there being a link.
"But to the best of my knowledge, no link was ever established. And certainly, in my dealings with the investigation later on, there was no link apparent to the other case at all."
The detective told the inquest that police had been unable to place Mr Whitworth and Mr Kovari together, which might have been expected had claims of a relationship made in the fake suicide note been true.
However, Det Insp Schamberger said police had done "work around social media" to check whether the Gabriel mentioned in the note was actually Mr Kovari.
"We believe it was the same person," he told the coroner.
But when Scotland Yard detectives later conducted the extensive murder inquiry they found no links between the two men.
http://www.bbc.co.uk/news/uk-38123896