The foremost question is wether your mother's Kindle is still linked to her Amazon account. Do you have access to her account to de-link it? You would have to log in with your mother's account here on amazon.de—or whichever Amazon country store she used—and de-link the Kindle under Your Account/Manage Your Account and Devices/Devices.
If you have done so or if your mother's Amazon account has been deleted already you should set the Kindle back to factory settings and then register it to your account by simply entering your Amazon customer's e-mail address and password on the Kindle. To do so you will need a WiFi connection at least once.
Please note that afterwards the Kindle is your device but you will not have access to your mother's e-books. Because e-book purchases are just licences linked to a person. This goes at least for copy protected e-books purchased directly at Amazon. If your mother had copy protection free e-books from other sources or personal documents on her Kindle you should by all means save the Kindle's document folder via a USB connection to your PC before setting the Kindle back to factory settings.