Welcome and thanks for your question.
I'm Todd and I will be the expert working with you today to help resolve your problem.
Because all Kindle data are stored on the Amazon account, it's very easy to transfer it to the new device. All you have to do is to register your new Kindle with the same Amazon account you have on the stolen one. As soon as you connect your new register Kindle to the wifi all books will automatically be transferred to the new Kindle.
Did you deregister your stolen Kindle?
If not please perform the procedure below to deregister your stolen Kindle. That way you will prevent thief to use your data.
To de-register your Kindle please follow the steps below:
1. Go to the web page below - click here to open web page
2. Log in using your Amazon account information
3. On the left side select "Manage Your Devices"
4. Find your device on the list and select it
5. When you select your device from the list "Deregister" option will appear.
6. Select "Deregister" and confirm it
Please don't hesitate to ask if you need more information. I will be happy to help with any follow up questions. You can also contact me when you receive your Kindle if you have difficulties to set it up.If you need more information please do not rate my answer negative BAD service or POOR service. Reply to me using "Reply to Expert" button and I'll provide you with more help.