Identify the movie before using the remote
Search on your phone or computer and note the year, cast and viewing service. On the television, open that service's supported app and find the same edition. Roku, Apple TV and Android TV have different app catalogs; a phone installation package does not become a TV app simply by sharing a name.
Cast from a compatible app
With a supported app and receiver, use the app's Cast control and choose the destination screen. The devices normally need the same Wi-Fi network. Google's casting instructions explain the equipment and connection requirements. If the receiver is absent, investigate that connection before changing the movie search.
AirPlay and mirroring
AirPlay can send video from a compatible Apple app to a supported receiver. Screen mirroring is a separate method. Apple's instructions cover both and note that some video apps do not support AirPlay. Use the service's TV app when that is the supported route.
Check dialogue, subtitles and picture from your usual seat. After finishing an episode, update the manual checkpoint on the browser where you keep your Flixtorz list. That reminder does not automatically read a TV app's playback history.