One film is a separate transaction
The publisher offers individual seventy-two-hour rentals without requiring an active subscription. Its FAQ places that transaction on the website. A television app that can play the catalogue need not also expose the rental checkout, and the absence of a rent button does not by itself establish that the title is unavailable as an individual rental.
Make the account handover visible
If you choose to rent, inspect the film and its current conditions on the official website first. After completing your own transaction, check the same account on the television. A receipt in one account and a different sign-in on the TV will not demonstrate that the app has lost a purchase. Compare the account identity privately before initiating a second payment or a new subscription simply to make the title appear.
Keep a rental issue separate from cancelling a subscription
A one-film rental and a recurring membership call for different follow-up actions. The FAQ provides separate cancellation routes for website, Android, iOS and Prime Video Channel subscriptions; those routes should not be applied automatically to an individual rental. If the film appears on the website but not the app, report that exact difference with the title and device. The supported-TV list and a general offline feature are not proof that every television supports downloading. We have not rented a film or tested the account transfer.