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Leak where conservatory joins roof

We have a leak coming through the roof where the conservatory joins the house. The conservatory is framed on 3 sides by the house/roof. The conservatory itself does not leak. The attached interior pictures have green lines drawn on them to show where the leak comes through (it leaks above the lines). The exterior photo shows the outside/roof. It seems like there should be something directing water away from the edges of the roof.