The frail-looking 78-year-old's trial began in March 2020, was adjourned for 14 months due to the COVID-19 pandemic ... but now it's come to a close with Judge Mark E. Windham sentencing him to life behind bars, ruling Durst's guilt was proven beyond a reasonable doubt in multiple ways.

Before the sentencing, Durst's legal team tossed up a Hail Mary for a new trial alleging several errors by the court ... but the judge shot it down.

After that, there was a round of emotional victim impact statements -- including one family member calling for Durst to reveal the location of Kathy Durst's body -- and Susan's son spoke at length about how her death negatively affected his life.

As we reported ... Durst was found guilty in the murder of his best friend, Susan, and he was facing life in prison without the possibility of parole.

The first-degree murder conviction and sentencing come more than 6 years after Durst arguably confessed to murdering Berman and his wife, Kathy, on a hot mic during the filming of the documentary, "The Jinx: The Life and Deaths of Robert Durst."

In the HBO doc, you hear Durst muttering to himself, "You're caught ... What the hell did I do? Killed them all, of course." He claims he was high on meth when he made the confession.

You'll recall ... Kathy disappeared way back in 1982 and it's widely suspected Durst killed her, though she was never found and he was never charged. Kathy's family filed a wrongful death lawsuit against Durst, but he scored a legal 'W' in that suit.

Los Angeles County prosecutors set out to prove Durst killed Berman because she knew something about Kathy's death. Berman's body was found on Christmas Eve in 2000, and just 2 days later, the LAPD received a letter from someone telling cops where Susan's body could be found.

Police said they linked the letter to Durst, but the case went cold ... until it was reopened in wake of the HBO doc.