@venutius: thank you! Not quite what I was looking for, but might work if there is nothing else.
@danbp: I notice that the Mass Messaging in Buddypress plugin hasn’t been updated for 2 years. Is it still safe to use?
General reflection: to me this seems like extremely obvious functionality (for an administrator to be able to message all users in a specific group). How come it isn’t part of Buddypress core functionality?
