Ahmaud's mother, Wanda Cooper-Jones, tells TMZ ... "We want all parties involved to go to prison for life." She says this includes the 2 current murder suspects -- Gregory and Travis McMichael -- along with the man who recorded Arbery's slaying, William "Roddie" Bryan.

Wanda tells us she and Ahmaud's legal team believe Bryan was involved in the fatal incident, but as we reported ... he claims he had nothing to do with it. However, he has not explained why he was recording.

For his part, Ahmaud's family's attorney, Lee Merritt, wants everyone involved in Arbery's death convicted and "appropriately sentenced."

Merritt believes Bryan should be prosecuted along with the McMichaels ... "because he actively participated in the ambush according to previous statements by the McMichaels” and “because our forensic expert says that he was likely holding and brandishing a firearm."

Merritt adds that for justice to be done, members of the Glynn County Police Department who initially failed to investigate Arbery's killing and make any arrests need to be held accountable.

He's also going after Jackie Johnson and George Barnhill, district attorneys involved in the case, for allegedly mishandling it at best ... or committing prosecutorial misconduct at worst.

Merritt tells us he believes Barnhill specifically should be disbarred by the Georgia State Bar, as well as removed from his position as District Attorney ... because of his role in both withholding information and actively attempting to taint the jury pool.

A new lead prosecutor has been appointed to the case by the Georgia Attorney General -- Joyette Holmes, the district attorney of the Cobb County Judicial Circuit.

Ahmaud's mom tells us Holmes called her to introduce herself and let her know she is taking over. Clearly, the expectations for her from Arbery's family are high.