I'm trying to understand the relations between the existance of Coriolis force and the conservation of angular momentum. I found this explanation on Morin. I do not understand the two highlighted parts. In particular it seems that Coriolis force is there to change the angular momentum of the person in the lab frame. But this cannot be true since Coriolis force is a fictitious force, existing only in the rotating frame. I don't see clearly the link between Coriolis force and conservation of angular momentum in this case. Can anyone give some further explanations about this?