What was the first movie sequel?

The Fall of a Nation (1916)

According to LiveScience:

"The Fall of a Nation," released in 1916, is considered the first feature-length movie sequel, according to "The Story of Hollywood: An Illustrated History" (BL Press, 2006). Directed and co-written by Thomas Dixon, Jr., the silent film is a sequel to director D.W. Griffith's controversial 1915 classic, "The Birth of a Nation." In his book, "The Birth of a Nation: A History of the Most Controversial Motion Picture of All Time" (Oxford University Press, 2007), author Melvyn Stokes writes that Dixon made the sequel to capitalize on the success of first film.

Dixon actually wrote a novel called "The Fall of a Nation" before he did the film. Much like its predecessor, "The Fall of a Nation" was and remains a controversial film, according to Turner Classic Movies, for its glorification of the Ku Klux Klan and promotion of many ugly stereotypes. "Viewed as propaganda, it is a pity it is so reckless," The New York Times wrote about the film after its screening in 1916 at New York's Liberty Theatre. The paper also called it a "lively, interesting and sometimes preposterous picture."

"The Fall of a Nation" is also considered a 'lost' film. Surviving prints of the movie disappeared decades ago and have yet to surface anywhere.

Sherlock Holmes II (1908)

There were earlier series of films. The earliest, according to Wikipedia's lists of film series, is Viggo Larsen's Danish 1908 silent series of Sherlock Holmes films:

• Sherlock Holmes I also known as Sherlock Holmes i Livsfare (Sherlock Holmes Risks His Life) (20 November 1908)
• Sherlock Holmes II aka Raffles' Flugt fra Fængslet (1908)
• Sherlock Holmes III aka Det hemmelige Dokument (1908)
• Sherlock Holmes IV aka Sangerindens Diamanter (The Theft of Diamonds) (30 April 1909)
• Sherlock Holmes V aka Den graa Dame (27 August 1909)
• Sherlock Holmes VI aka Droske 519 (20 January 1910)

After leaving Danish film company Nordisk, he joined German film company VitaScope and made five further Sherlock Holmes films under the title of Arsène Lupin contra Sherlock Holmes (1910), followed by Sherlock Holmes Contra Professor Moriarty (1911).

For feature films, it likely was AN HOUR BEFORE DAWN (1913), as it had the same characters such as star as Kate Kirby as CHELSEA 7750 (1913). THE PORT OF DOOM (1913) also featured Kate Kirby. At four reels, these features were short -- less than an hour.

In the early 1910s, Biograph Films refused to allow their chief director D. W. Griffith to make films longer than one reel (about 10-12 minutes). So Griffith made two films that were released separately, and you could consider these sequels. That these films were popular at the box office certainly helped other studios (not Biograph) decide to make longer films. Examples are HIS TRUST (1911) and HIS TRUST FULFILLED (1911) & ENOCH ARDEN, Part 1 (1911) and ENOCH ARDEN, Part 2 (1911).