Hand over from scrum master

Where is executive sponsorship for agile change coming from, and what can you do to secure me access to key influencers before you go?

The Age of Product site has a list of questions for many situations that should be helpful to you. 

Is this team effective? 

That is all I would ask. Then I would let the team know that they should continue to work as if the Scrum Master has gone on an extended vacation that spans 2 of their Sprints while you observe how they work.  At the end of your "extended vacation" start to interact with them as they need help.  In a successful Scrum Team, the Scrum Master shouldn't be required to do a lot of work.  The team should be able to handle self-organization and produce value.  You aren't there to manage their work.  You are there to help them be better at the work they do.  So find out what you can do to help them by seeing what they struggle with when their current Scrum Master is not available.  Don't try to be their previous Scrum Master.  Be their current Scrum Master and do what they need.  

Thanks guys! 

I would always advise Scrum Masters to continuously try to understand their role (and Scrum in general) from the perspective of Empiricism, and how the various aspects of Scrum relate in some way to Transparency, Inspection and Adaptation.

For instance: what would a Daily Scrum be like without Adaptation? What does a Product Owner adapt? What conversations are not taking place; and does that indicate a lack of Transparency, or a lack of Inspection?

You might find at some point that your colleagues realize what you are doing, but not why. For instance they might see that you always encourage conversations to take place with certain people present, but they might not realize this is you attempting to increase Transparency, in order to allow better Inspection and therefore more relevant Adaptation.

I agree that observation is a good starting point, then as you start to act, be careful to ensure at least the Scrum Team and those in leadership positions have a good understanding of your motives. For example, if you find that the Scrum Team are not always having Sprint Retrospectives, it can be a lot more effective to approach that from the perspective of missed opportunities to make problems Transparent, to Inspect the situation, and Adapt towards doing things better; rather than simply stating that a Sprint Retrospective must take place, which might lead to resentment, or people viewing you as the "Scrum Police".