Edit: There is now an entry for this in the ArcGIS Ideas area. If you want it, vote it up... https://community.esri.com/ideas/12098.
How can our organization's Portal for ArcGIS users search, find, and use publicly shared ArcGIS Online items within their Portal for ArcGIS environment?
I found Derek Law's post https://community.esri.com/docs/DOC-3385 which contains a PDF which says:
ArcGIS Online Content
Portal for ArcGIS also provides access to all nine basemaps available from ArcGIS Online: Imagery, Imagery with Labels, Streets, Topographic, Terrain with Labels, Light Gray Canvas, National Geographic, Oceans, and OpenStreetMap. Optionally, premium content from ArcGIS Online can also be used with Portal.
So there's that - basemaps and premium content.
Short of adding, describing, and styling each publicly shared ArcGIS Online item to Portal, have you found a way to configure Portal to return publicly shared ArcGIS Online items when a user searches for them?
We're at Portal 10.3.1.
thx!
tim
Solved! Go to Solution.
Hi Zachary,
Nope, no ArcGIS Pro in my original post. I just tested your desire successfully in ArcGIS Pro 2.4.2. Here's what I did:

cheers,
tim
Right. So you have to switch back and forth from AGO to your Enterprise Portal for each search, right?
Which is odd because when you're in the map viewer in Portal you can choose either from the drop down.
Maybe I'm missing something in Pro? Using latest release.
Maybe. Try some things out until you find your happy place. Let us know how it went.
tim
Users seem to be confused because in Portal they can search for Portal items & ArcGIS Online items intuitively. 
(Presuming you've configured your enterprise site to allow ArcGIS Online content of course).
In Pro you need to log out of Portal and log into ArcGIS Online. This presumes all of your user base has an ArcGIS Online account in addition to their Portal accounts, whereas in the Portal configuration this is not necessary.
Nice evaluation and summary. It looks to be a good candidate for ArcGIS Ideas. Also, in my test, I didn't have to sign in to ArcGIS Online in order to make it my active portal, search, find, and use content. Of course, this is only the case with any content that is shared to everyone from ArcGIS Online.