After having collected enough information during the assessment period of an Agile coaching engagement, especially using interviews, an Agile Coach should be in a position to draw a Process Map of whatever has been discovered.
You could go use a tool to build a clean and elaborate process map but I recommend starting with stickies. Take a bunch of stickies and write down the important activities that you know different roles get involved in during the start of an iteration, at the end of an iteration, and in-between. Give a short name for the activity and note the name of the role as well. Keep the granularity at medium level, as you don't want too many stickies at once, at least not initially.
Now on a whiteboard, sequence these stickies, one at a time, in the order they are done. Draw connecting lines between the stickies as you proceed. If some activities are repeated, draw loops accordingly. You will now have a visual timeline of an iteration. If you can spot obvious gaps in the timeline, add more stickies for those missing activities along with role participation.
Now you will want to know more about what feeds into an iteration and how, and what goes out of an iteration and how. The former is usually around requirements and defect management. The latter is typically about releases and deployments. In most organizations, customer feedback and customer support connects the end point to the starting point. However, some of this could be just your assumption. It is unlikely you'd have gotten a complete view of the process as some of these aspects are not apparent mid-release nor are all team members aware of them. It is time to get proper validation.