On the afternoon of April 4, Ray checked into a boardinghouse in Memphis, with a bar called Jims Grill on the first floor. He paid $8.50 for a weeks stay. The rear of the boardinghouse faced the Lorraine Motel across Mulberry Street.
According to the criminal justice system of the state of Tennessee, James Earl Ray fired the shot from the second-floor bathroom of the boardinghouse. He then grabbed some belongings in a blanket, stashed the rifle in it, left the building and dropped the bundle in the doorway of a nearby building.
He drove away in a white Ford Mustang before the area was barricaded, went to Atlanta and then to Canada and England before being arrested in July 1968.
That Ford mustang is owned by a collector of mustangs east of Atlanta. To my knowledge it has never been put on display.
He almost got away with it. His plan was to fly to Rhodesia where he believed he would be treated as a hero by the Apartheid gov't of Ian Smith (in truth, they would've likely extradited Ray back to the United States).
Excellent page-turner of a book about the King assassination and ensuing manhunt: