Erased HD using recovery, attempted to reinstall OS X but no disk available

Attempting to factory reset so that I can give my old iMac away. Followed Option+R restart, used disk utility to erase HD and HD data. Then shut down, forgetting to go back to Recovery screen to reinstall OS X. So restart again using Option+R and hit reinstall OS X but no drive is visible to load it to. So, then I connected an external HD, and got OS X on it then used this as startup disk. How do I get the internal HD visible and get OS X transferred from external HD to internal HD??