"Unable to connect to synchronisation service after installing Azure AD Connect" error comes up if you try to launch Synchronization Services Manager straight after installing Azure AD Connect.
Unable to connect to the synchronisation service. Some possible reasons are:
The service is not started.
Your account is not a member of the required security group.
The issue comes up when the admin gets all excited to configure the sync service straight after the installation, missing a key bit of information that comes in the documentation ;)
The admin account has to be a member of the local group named "ADSyncAdmins".
Solution is to make sure that the admin account is a member of the local group "ADSyncAdmins".
Then log off from the AAD Connect server before launching the Synchronization Services Manager. Even if you are a member of the group, only a logoff and logging back will updated the token.