Your phone is a good place to start
Cinezone2 opens in a modern mobile browser. Search at the top, switch between movies and series, then tap a poster for the title details. My List works in that browser without creating a separate account.
Adding a home-screen shortcut
Use your browser's Add to Home Screen or installation menu when it is offered. Open the shortcut afterwards to check that it reaches the right site. The menu varies between Android, iPhone and browser versions.
Is there a Cinezone2 APK download?
There is no native APK installer supplied here. The mobile website and a browser shortcut are the available ways to use this catalogue. Neither should be confused with an Android package advertised on another domain.
Before changing phones
Save a text backup from My List while the old browser is available. Merge that backup on the new phone to bring recognised titles and episode reminders with you. A browser shortcut by itself does not move stored choices.