This article explains how to activate the Outreach integration. You need the same admin on both platforms (Postal & Outreach) to enable the integration. Integration only works for users with licenses to both platforms.
Activating the integration in Postal
Go into Profile Settings and click 'Integrations'
Find the Outreach logo and click 'Connect to Outreach'
Select the boxes that match best for what you would like to sync from Outreach.
Activity from Postal will sync back to Outreach on the contact level
To start sending one-offs while working in Outreach, you will need to download the Postal Everywhere extension.
Now it's time to create Triggers for Outreach.