How download movie from Apple TV app onto iPhone?

From the article linked to above:

Download a show, movie, or event on your iPhone, iPad, or Mac

1. Open the Apple TV app on your iPhone, iPad, or Mac.
2. Browse or search for a TV show, movie, or event.
3. Choose the show, movie, or event, then choose the Download button.
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6. To find and play your downloads, go to the Library tab, then choose Downloaded.
7. Can't download a show or movie? You might have reached the limits for downloads, or the channel might not allow downloads.*