Answer by taking a quote from the following article:

Carter was born in Clifton, New Jersey, the fourth of seven children. He acquired a criminal record and was sentenced to a juvenile reformatory for assault, having stabbed a man when he was 11. Carter escaped from the reformatory in 1954 and joined the Army. A few months after completing infantry basic training at Fort Jackson, South Carolina, he was sent to West Germany.

During the new trial, Alfred Bello repeated his 1967 testimony, identifying Carter and Artis as the two armed men he had seen outside the Lafayette Grill. Bradley refused to cooperate with prosecutors, and neither prosecution nor defense called him as a witness.  The defense responded with testimony from multiple witnesses who identified Carter at the locations he claimed to be at when the murders happened. Investigator Fred Hogan, whose efforts had led to the recantations of Bello and Bradley, appeared as a defense witness. Hogan was asked on cross examinations whether any bribes or inducements were offered to Bello to secure his recantation, which Hogan denied. His original handwritten notes on his conversations with Bello were entered into evidence. The defense also pointed out the inconsistencies in the testimony of Patricia Valentine, and read the 1967 testimony of William Marins, who had died in 1973, noting that his descriptions of the shooters were drastically different from Artis and Carter's actual appearances.  The court also heard testimony from a Carter associate that Passaic County prosecutors had tried to pressure her into testifying against Carter. Prosecutors denied the charge. After deliberating for almost nine hours, the jury again found Carter and Artis guilty of the murders. Judge Leopizzi re-imposed the same sentences on both men: a double life sentence for Carter, a single life sentence for Artis.  Artis was paroled in 1981. Carter's attorneys continued to appeal. In 1982, the Supreme Court of New Jersey affirmed his convictions (4-3). While the justices felt that the prosecutors should have disclosed Harrelson's oral opinion (about Bello's location at the time of the murders) to the defense, only a minority thought this was material. The majority thus concluded that the prosecution had not withheld information that the Brady disclosure law required that they provide to the defense.  According to bail bondswoman Carolyn Kelley, in 1975-1976 she helped raise funds to win a second trial for Carter, which resulted in his release on bail in March 1976. On a fund-raising trip the following month, Kelley said the boxer beat her severely over a disputed hotel bill. The Philadelphia Daily News reported the alleged beating in a front-page story several weeks later, and celebrity support for Carter quickly eroded, though Carter denied the accusation and there was insufficient evidence for legal prosecution. Mae Thelma Basket, whom Carter had married in 1963, divorced him after their second child was born, because she found out that he had been unfaithful to her.

When did his appeal begin?
Carter's attorneys continued to appeal. In 1982, the Supreme Court of New Jersey affirmed his convictions (4-3).