Today, HubSpot doesn't allow app partners to link to the conversations inbox, but we can add sms through an email flow.
This is accomplished by triggering an email to be sent to your HubSpot inbox email address every time a new SMS is received. This will then be visible in your conversations inbox.
1. Add the email address used for your HubSpot inbox as a user in your Sakari account. This article walks through how to add a new Sakari user: Add a New Sakari User
2. Turn on email notifications when a message is received. This article walks through how to add a new Sakari user: Enable SMS Email Notifications