as described in your stackoverflow link; you’ll see step 4:
setTwitterAuthData(…)
This would basically be a javascript function that you define in the main page.
This function does not exist: you will have to create it and make it do something.
The pop-up can call this function on the original window. In the function you might store the OAUTH to a database or to a (global) variable.
This way you can now access it in the rest of your page.