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Do the power door locks work? If the power locks work ok with the switch inside but the not with the key fob then the key fob itself is likely the case. I'm assuming the power locks do work with the switch since you didn't mention them not working. Since you trunk does open with the fob you know the car is receiving the signal from it.
What I would recommend is having the fob tested. Most shops and dealers will have a tester that can test it's output signal, large parts stores like Autozone will test them for free. I believe you will find that it transmits a signal when pressing the trunk release button but does not when pressing the lock and unlock buttons. If that's the case then the fob will need to be replaced.
Power lock with switch inside lock all the door bath not unlock’light is answer to fob.What is mean ?
The power door lock button lock all the door bath not unlock