I believe if you make the user a Business Manager for the process they will have access via Monitor tab for the process.

From the Administration Guide

Users can have one of the following roles for a process:

• The Process Admin can modify the business process, see its results, and create reports for it. They can also reassign tasks from the results page. Additionally, process admins have the Submitter rights below.
• The Business Manager can start processes; see its results, view, create, edit, and share reports; take snapshots; edit process instance names; cancel process instances; and complete and reassign tasks. Business managers cannot design processes or delete instances.
• The Submitter can start processes, either by submitting a form or by starting a process manually. In the Completed Tasks section under My Tasks, submitters can also see information about processes they have participated in.