Local 98 was already at or near the city's $10,600 limit for contributions from political-action committees for Green and Rubin in that election, the report said.
The board took testimony under oath from Spencer and his campaign manager, political consultant Mike Fleck, and concluded they could not offer a "credible explanation" for Spencer's contributions to Rubin and Green.
"The simultaneous swap of funds between Local 98 and [Spencer's campaign] and the contributions to the candidates, just four days before the election, can only lead to the conclusion that it was part of an agreement with Local 98, [Spencer's campaign] and Fleck to funnel additional contributions from Local 98 to Rubin and Green in violation of the Philadelphia Code of Ethics," the report said.
The report has been forwarded to the Philadelphia Board of Ethics and the Berks County District Attorney's Office.
Rubin dismissed the report, saying, "There's nothing there."
Green expressed confidence that the Board of Ethics will pursue the issue if it "thinks someone did something wrong."
John Dougherty, Local 98's business manager, denounced the report as a "partisan witch hunt."
"This is two white tea-party commissioners chasing an African-American mayor," Dougherty said. "There's nothing illegal with this."
The three Berks County commissioners serve as the Board of Elections. The commissioners, including one Democrat and two Republicans, unanimously approved the report.
"I can't dignify such a pathetic comment with a response," Berks County Commissioner Mark Scott said when told of Dougherty's claims. Scott is chairman of the Board of Elections.
On Twitter: @ChrisBrennanDN