With the Share Research option selected, Aurora will share any new discoveries you make with the NPR. It will NOT share the prerequisites, though this ahouldn't prevent the NPR from using the new technology.
There is also (somewhere on the Diplomacy screen) an option to 'Give Tech' to another race. You can use this to fill in background techs.
If you and the NPR each have a (big enough) colony on the same world, then the 'lesser technology osmosis' will give each other any tech that is three(? I think) or more levels lower than a newly discovered tech.