Hello Charles,
It order to send content in both directions it is necessary to set the collaboration workspace to send and receive.
Send only:
When the host selects Send as the access mode for the guest, the guest can send content to the host but does not receive any content from the host.
Receive only:
When the host selects Receive as the access mode for the guest, the guest will receive content from the host but cannot send any content to the host.
Send and Receive
When the host selects Send and Receive as the access mode for the guest, the guest can send content to, and receive content from, the host. With each sync of the collaboration workspace, content will be updated to match how it exists in the portal of origin. The Send and Receive access mode cannot be used to handle back and forth editing of a single dataset between host and guest.
If you are still not receiving any items from ArcGIS Online when the collaboration workspace is set to Send and Receive there may be additional issues with the collaboration.
I hope this helps!
Thanks,
Thomas.