Help me understand Motorcraft 12v battery warranty

Long story short: I bought a used Lincoln from a dealer in another state back in 2024 and they had replaced the 12v Motorcraft battery as part of the CPO program. Now, unfortunately, the battery is starting to fail and trying to get it replaced under the warranty; however, my dealer told me that I can’t request a replacement as I was not original owner of the battery when it was purchased in 2024 originally.

On the hand, the dealer I bought the car told me that the warranty follows the battery, not the owner. I am lost on what should I do? Because apparently my dealer can’t do the warranty replacement and they told me only the original owner can request it when it is the dealer I bought the car from.

PS: Sorry if this is not the right sub to post my question, but just trying not to spend money on a new battery if it can replaced under warranty