It happened just after 9 p.m. Sunday at the Wells Fargo Bank in the 4500 block of Raeford Road.
Police said 24-year-old Anna Williams was in the passenger seat of her friend's car and was attempting to make a deposit when a man approached and shot her through the back. Family members said the bullet went through her back and damaged her liver and stomach.
Police said Thursday detectives have identified the suspect as 21-year-old Ladarious Dion Hill of Sexton Court in Fayetteville.
Wednesday night, members of the FPD Gun and Gang Violence Unit arrested Hill on a warrant for assault with a deadly inflicting serious injury with intent to kill and robbery with a dangerous weapon. Hill was in the Cumberland County Detention Center under a $100,000 secured bond.