I understand you're looking for a way to integrate external inbound email into your Jive inbox. Unfortunately, this isn't available at this time and may require customizations to integrate. If this is an important feature you'd like to investigate, I would recommend working with Jive Professional Services to scope for feasibility. Otherwise, I would encourage submitting a feature request idea in the Ideas for Jive space to help capture this for our Product Team.
Let me know if you had any other questions.