Hope my explanation is clear below. If not you search some YouTube videos
There two routes you can go. You can. Find a Dremel and cut a hole in the back plastic piece of the otterbox defender. Or you can do my method. (YouTube has videos on modifying a S4 with cutting, same idea with note 3 to give you some idea)
Otterbox defender comes with 3 pieces, two inner plastic pieces and the outer softer TPU shell
For use with the Anker extended battery, use the back cover of the phone that came with Anker. Now use the front plastic piece that came with otterbox, that goes over the front of the phone but do NOT use the back plastic piece
Then put the outer rubber TPU otterbox over the phone. Will be a tight fit but fits perfectly
Now you have all the otterbox protection with the 6400 mah extended battery too. And I can attest it protects the phone. My kid threw my phone, in this setup, against the wall. My tempered glass screen protector scattered but phone was perfect. I replaced the screen protector. And the actual screen was perfect too!
Hope that makes sense. If not let me know. You Can always cut the back plastic piece instead but I thought that was too much hassle
sent from my Galaxy Note 3 via Tapatalk