One significant milestone in the development of the cinema screen was the invention of the reflecting cinematograph screen by Robert William Paul in 1896. This screen utilized a combination of a concave mirror and a translucent screen, which enhanced the brightness and sharpness of projected images. Another notable contribution came in 1913 when C. Francis Jenkins and Thomas Armat developed a lenticular screen, which featured a structured surface with tiny ridges, allowing for wider viewing angles and improved image quality.
The use of silver-coated screens for enhancing reflectivity became popular in the 1920s, and the concept of curved screens for providing a more immersive viewing experience was introduced in the late 1950s. Further innovations in screen materials and technologies, such as high-gain screens, micro-perforated screens, and rear-projection systems, continued to shape the development of cinema screens over the decades.
Therefore, it can't be narrowed down to a specific year as the invention of the cinema screen was a result of a series of incremental improvements and advancements in the field of motion picture projection throughout the late 19th century and beyond.