If you move a topic from A to B that the user already read, there won’t be any notification.
If you move a topic from A to B the user didn’t read, there will be, in some cases, an edit notification. In others, a new topic notification.
It may send an edit notification when the topic is partially read, and a new topic notification when we didn’t read it at all.
Moving a partially read topic with unread replies (edit notification):
Moving first a read topic (no notification), then an unread topic (new topic notification):
If the user had been watching category A (and B) and had already received a new topic notification for the topic when posted in category A, will a further notification (whether “edit” or “new topic”) be sent when the topic is moved to category B?
I think I can infer from your answer that it will, but I just want to check.
If the user didn’t read the topic and has the notification as unread in his notification menu, there won’t be any additional notification. What will happen is that the current notification will be removed and almost instantly replaced with a new one.