Welcome and thanks for your question.
I'm Todd and I will be the expert working with you today to help resolve your problem.
Yes, you can transfer books from your old to your new Kindle. Your books are stored on the Amazon cloud, so all you need to do is to register new Kindle using the same Amazon account you have on your old Kindle. After registration of new Kindle all your books will be transferred on your new Kindle.
Be sure that your new Kindle is connected to wifi internet. After registration, from Home, tap the Menu icon (3 lines icon), and then tap "Sync & Check for Items".
You can transfer only specific books manually using procedure below (be sure that your Kindle is registered and connected to wifi).
1. Go to the link below (use your Amazon username and password ***** log in) - click here
After log in you will be prompted with the "Manage Your Content & Devices" page (check the picture below)
2. Find the book you want to transfer to new Kindle and select it.
3. On the left side, click on "Actions" and select "Deliver".
4. Find you new Kindle on the list and select it. Confirm using yellow "Deliver" button.
5. On new Kindle, from Home, tap the Menu icon (3 lines icon), and then tap "Sync & Check for Items".
Please don't hesitate to ask if you have any difficulties. I will be happy to help with any follow up questions.If you have any difficulties or 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.