Thanks to the humanity6 Twitter account we now know the official release date of the upcoming third film in the Fate/stay night: Heaven's Feel series. The third movie with the subtitle Spring Song will be out in spring 2020. There is no other information or a specific month for the release.
Fate/stay night Movie: Heaven's Feel - II. Lost Butterfly premiered on January 12 in Japan and is the second title in the trilogy produced by Ufotable. This film is developed by the same people from the previous and first film. It is directed by Tomonori Sudo, Hikaru Kondo produces it, Akira Hiyama writes the script, Yuki Kajiura develops the music and Aniplex of America holds the English license.
The first film in the trilogy, Presage Flower, aired on October 14, 2017 with 120 minutes or run-time. Lost Butterfly is the fourth adaptation developed from Ufotable's Type-Moon works. The Kara no Kyokai films were the first, then we got the Fate/stay night television series and finally the Unlimited Blade Works anime series.
Fate/stay night: Heaven's Feel Spring Song is out on spring 2020