At least the French patent was seemingly granted earlier:Edison's patent on the kinetoscope was granted in 1897 with "Application filed August 24, 1891. Serial No. 403,534. "
https://de.wikipedia.org/wiki/Léon_Guillaume_BoulyLéon Guillaume Bouly (* 1872, † 1932) is accepted as a French inventor, who was the originator of the name Cinématographe. On February 12, 1892, under the name of the application filed for a patent on an "appareil reversible de photograph et d'optique for the analysis and the synthesis of the mouvements, the Le Cynématographe Léon Bouly". It came to the French State Patent, number 219'350. On December 27, 1893, a change was made to the name of his apparatus: Cinématographe.
The Cinématographe works with paper and roll film without perforation on the principle of the clamp. The film drive is accomplished with a segmented roller opposite full roller.
When in 1894 the annual fee for the patent had not been paid, the term Cinématographe became common property and in the following year reserved for the brothers Lumière.
translated by Google, sorry for the laziness
And even Anschütz has been earlier:
https://de.wikipedia.org/wiki/Ottomar_Anschütz + GoogleIn the summer of 1886 Anschütz was commissioned by the Prussian Ministry of War to "take chronophotographies of riders and horses of the Military Riding Institute in Hanover, in order to enable the development of scientific instruction methods for the cavalry school."  The 24 electrically interconnected cameras made motion studies he combined to image series. Other series show human movement studies.  In 1886 he developed a device for the projection of his series images, which consists of a disk with a diameter of 1.5 meters and 24 glass plates in the format 9 cm × 13 cm. The photo plates illuminated from behind with a Geissler tube are rotated by a crank drive at a speed of 30 frames per second. In 1887 he presented his "electric speed-watcher" - the electro-tachyscope - in the Ministry of Culture in Berlin. Siemens & Halske began commercial production of the device in Berlin, which was widely used from about 1891.
I think this is a case of parallel discoveries and a matter of definition, which version one is willing to accept as a functioning projector.
I'm notoriously skeptic when it comes to this Edison hype. In my opinion it often doesn't hold the proof. (Opinion: The only aspect of his I admit he was better than his competitors, was his marketing and self glorification skills.) As I read the articles about Edison, it is mainly (French born!) Dickson who deserves the merits, but this is also nitpicking, as he had been Edison's employee.Unlike Dickson, the Lumières used 35mm film, simple perforation and transporter.