In the Scrum Guide the ROLE of Functional manager is not specifically defined. As scrum focuses more on the self-organization more of Functional Manager involvement is not required if they do so, then the team is not following the correct way of Scrum.

• Functional Managers usually retain the job of assigning individuals to projects. They will be expected to continue to make these decisions based on the competing needs and career aspirations of individuals, locations etc.
• In few organizations the role of a functional manager is accustomed to assigning roles to the individual which now after transition they will not be able to do that as an individual selection of work is a fundamental aspect of how the team self-organize and must be left with the team.
• They should now start working in the bottom-up approach. The manager should say “Here is our purpose and direction-I will guide and coach.”
• They also retain the responsibility for developing the people in their GROUPS. Securing the budget and time, encouraging them for innovations, challenging them, build the leader in them are all PARTS of the functional manager role.
• They also retain the role of HIRING and firing decisions which not even scrum master and product owner has this level of authority.
• Writing periodic reviews by taking the INPUTS from coworkers is also the prime responsibility of the functional manager and they will continue to retain them.
• They can also attend sprint reviews and even quarterly planning meetings.