If a team already practices Scrum method successfully, how does the Scrum Master participate in further development? Will he/she continue to fulfill the same responsibilities?
There is more than one question here.
You can check the Scrum website for the 'by the book' definition of the Scrum master role, which includes a whole tonne of general management, consultancy and project management stuff in it. Plenty to fill a FTE.
Then you have the reality of most work places, where the Scrum Master is seen as a consultant position which can be dropped after you have switched from whatever you were doing before to scrum, or filled by a random employee, say the lead dev or a project manager, if you don't want to hire a consultant.
And then you have the career advice aspect 'I'm a scrum master but my team don't need me' question.
I think like any job, the title doesn't really define the role. It's down to the individual to carve a niche in the system.
The Scrum Master is a coaching role. Lyssa Adkins borrows the Shu-Ha-Ri approach from Aikido when talking about coaching teams. (I only know this model from coaching, I have no idea how faithfully it's adopted).
Early in Scrum maturity, the team is in the Shu level. They need to understand how the mechanics of Scrum work, develop discipline in the practices, and learn how to be effective in the new approach. The Scrum Master acts as a guide in these areas.
In the Ha level, the team understands the rules of Scrum and wants to bend them or expand on them to adjust the method of working to their needs. Here, the Scrum Master helps the team structure these experiments and drives transparency so that the team gets the most out of these improvements.
Finally, in the Ri level, the team has a deep understanding of how and why Scrum works and can apply these principles to develop completely new and novel ways of working. The Scrum Master here acts in a purely coaching role, stimulating and encouraging the team in their thinking.
There is no timeline for this. If the team has never followed Scrum as recorded, they've never really settled into the Shu level. Similarly, if they have always stuck by the rules, they've probably had this level mastered for a long time, but never moved on.
This is just in coaching the team. Of course, there is a whole organization around the team to work with. This checklist shows some things the Scrum Master can be working on each day with and around the team: http://scrummasterchecklist.org/pdf/ScrumMaster_Checklist_12_unbranded.pdf
The checklist is by no means comprehensive, but gives a taste of the many things a scrum master can be doing to help the team.
The scrum master in such a scenario will need to spend less time with the team, freeing them up to be able to work with two or three teams at the same time.