The offer for Apple TV+ from Apple should be available for 90 days, from the moment of registering the qualifying Apple device, regardless of the offer message showing. The message with the offer is just a reminder and shortcut. To claim the offer within the available timeframe, you can go to the Apple TV app on that new qualifying Apple device and find the “Enjoy 3 Months Free”-button there.
The offer for Apple TV+ might also be available from select partnering companies, with qualifying purchases from them. They will have their own terms and conditions, timeframe, and redeem method.
Read here how to redeem Apple’s offer: Apple TV+ offer - Apple
Read here about the conditions: Apple TV+ offer - Terms and conditions - Apple
Read here if you have trouble redeeming: If you can't redeem your promotion for an Apple subscription - Apple Support
Note that for Macs, users have to additionally sign in to the TV app (menu Account), for the redeem option to appear.
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If you had the trial subscription and you have canceled that prematurely, then the remainder will be forfeited.
