The ember coffee mug (not travel mug) has a EVE B0664-LF 7.2 volt Li-ion Battry. To replace the battery you simply* twist the mug base 15 degrees clockwise looking at the bottom and pull it away from the cup body. There is a ribbon cable that connects the base to the body that you need to remove. Once fully seperated from the body four screws secure a battery shield and once removed the circuit and battery can be removed.
* My use of the word simply really does not apply here. You will need to make a special fitted tool perhaps that will create enough friction on the base to turn it past the clips that secure it to the body. In addition you will need to pull the base away from the body in some way being careful not to damage the ribbon cable that connects the base to the cup body.