Like spikeyxxx mentioned, you can go ahead and utilize the Follow Active Quads method as explained at timestamp 15:50. That should normally get you most of the way!
However, if for some reason that doesn’t seem to be doing the job, you can manually edit UVs like you would a mesh. Make sure you are in Vertex selection mode in your UV editor (top left corner) and you should be able to move any vertex you’d like. 🙂