I found the answer to my own question in a biography posted on the U. of S. MS. website: Here it is, in case anyone else is interested:
Alex J. Postlethwaite was born on January 23, 1813, the son of Henry and Elizabeth Postlethwaite. Records indicate that Henry and Elizabeth had at least six children.
Originating from Pennsylvania, the Postlethwaite family had strong ties to the business communities of Philadelphia and Carlisle. In 1800, Henry's brother, Samuel Postlethwaite, traveled south into Kentucky and the Mississippi territory. On arriving in the Natchez district of Mississippi, Samuel decided to settle in the area, and by 1802 had established the first Postlethwaite store in the town of Natchez. Samuel married Ann Dunbar, daughter of William Dunbar, on March 9, 1803, and soon afterwards, Henry joined his brother from Pennsylvania. Within a few years the Postlethwaites headed numerous business ventures in the area, including the Bank of Mississippi and the Natchez Steamboat Company. By 1820, the family had become wealthy merchants, residing in a Natchez home known as "Clifton." Henry and Samuel both died of yellow fever in 1823 and 1825, respectively. Following the death of Samuel, the Postlethwaite family sold "Clifton" to the Surget family and moved to "King's Tavern" (also in Natchez), where descendants of the Postlethwaite family have lived for 150 years.
A.J. Postlethwaite followed in the footsteps of his father and uncle and also earned a living as a merchant in the town of Natchez, where he operated a dry goods store and import business. Associates and patrons of the Postlethwaite store included such notable names as Frederick Stanton, the Surget Family, and the Dunbar Family. Frederick Stanton (b.February 16, 1794) originated from Belfast, Ireland and arrived in Natchez with his brother, David in the early 1900s. Married to Hulda Laura Helm (b.February 1, 1807 - d.September 2, 1893), Stanton became one of the most prominent figures in Natchez during the nineteenth century, owning 444 slaves and 16,000 acres of land by the time of his death on January 4, 1859. He also built the family home "Stanton Hall" in 1857, which is now a popular tourist site for visitors to Natchez.
Of Postlethwaite's other associates, Francis Surget, Jr. was also a prominent member of the Natchez community. Married to Charlotte B. Linton on March 30, 1848, Surget was a multi-millionaire by the time of his death in 1866, leaving an estate worth approximately $1.5 million and 93,000 acres of land.
A.J. Postlethwaite never amassed such fortunes as Stanton and Surget, but remained a member of the wealthy and prominent Postlethwaite family, successfully running the dry goods store and import business throughout his life. A bachelor until the age of 38, Postlethwaite married Mary Elizabeth Browder (b. July 21, 1821) on February 19, 1851, and at least five children were born of the union.
Alex J. Postlethwaite died on December 31, 1866. Mary Elizabeth Postlethwaite, who outlived her husband by 34 years, died in Natchez on November 7, 1900.
Kane, Harnett. T. Natchez on the Mississippi. New York: William Morrow and Company, 1947.
Monuments in the Natchez City Cemetery. Natchez, Mississippi: McDonald's Printers, 1982.
United States. Census Schedule of Population. Mississippi 1850-1880, 1900.