The only way to get SSO functionality with two separate applications is to use PingFederate. Configuring PingFederate with Integrity is outside of the knowledge of the Navigate team, and you should ask that question on the Integrity board.
The concept is that you perform user authentication with PingFederate, and then authentication to any configured application is handled as SSO by PingFederate. That would get you the functionality you describe, but will be outside of the use case that is the basis for the Navigate instructions. You may need an engagement with PTC Field Services for something that complex.