Crime Alex Murdaugh Will Appeal His Conviction, Lawyer Says He's Victim of 'Vitriol and Misguided Attacks' "This is the next step in the legal process to fight for Alex's constitutional right to a fair trial," Murdaugh's defense attorney Dick Harpootlian tweeted By Corin Cesaric Corin Cesaric Corin Cesaric is an Associate Editor at PEOPLE. They have been working at PEOPLE for one year. People Editorial Guidelines Published on March 10, 2023 10:45AM EST Alex Murdaugh. Photo: Uncredited/AP/Shutterstock One week after Alex Murdaugh was convicted of murdering his wife and son, his lawyers announced they are appealing the conviction as well as his prison sentences. Murdaugh's defense attorney Dick Harpootlian announced on Twitter on Thursday that he and Jim Griffin have filed a notice of appeal. "This is the next step in the legal process to fight for Alex's constitutional right to a fair trial," his tweet reads, in part. "No amount of vitriol or misguided attacks will stop us from pursuing due process for Alex to the fullest extent of the law," Harpootlian continued in a follow-up tweet. Want to keep up with the latest crime coverage? Sign up for PEOPLE's free True Crime newsletter for breaking crime news, ongoing trial coverage and details of intriguing unsolved cases. Last Friday, Murdaugh was sentenced to two consecutive life terms in prison by South Carolina Judge Clifton Newman. Harpootlian — who is also a member of the South Carolina Senate — tweeted on Wednesday that he looked forward to working with Griffin during the appeals process and wrote: "To the naysayers-you have a misunderstanding of our justice system, I suggest you read the Constitution." Alex Murdaugh's Brother Says Convicted Murderer 'Knows More Than What He's Saying' About Killings The Notice of Appeal, which was obtained by PEOPLE, reads: "Richard Alexander Murdaugh appeals his convictions and sentences in the cases referenced above. The sentences were imposed by The Honorable Clifton Newman on March 3, 2023." It was submitted by Harpootlian, Griffin, Phillip D. Barber and Margaret N. Fox, the attorneys for Murdaugh. Everything to Know About the Murdaugh Family Murders, Including Alex's Conviction On March 2, Murdaugh was found guilty of fatally shooting his wife Maggie and son Paul in 2021 after a lengthy trial that was chock-full of eyebrow-raising moments. RELATED VIDEO: Alex Murdaugh's Brother Says Convicted Murderer 'Knows More Than What He's Saying' About Killings During the trial, a bomb threat interrupted proceedings, prosecutors played a video from Paul's phone that placed Murdaugh at the murder scene on the night of the killings, Murdaugh admitted on the stand to lying to authorities about his whereabouts that night and his surviving son Buster took the stand in his father's defense. Alex Murdaugh Admits on Stand to Lying to Police After Murders of Wife, Son: 'What a Tangled Web We Weave' The jury deliberated for less than three hours before convicting Murdaugh. Moments before sentencing Murdaugh, Judge Newman who oversaw the trial, addressed the convicted murderer, saying, "I know you have to see Paul and Maggie during the nighttime when you're attempting to go to sleep. I'm sure they come and visit you."