Should the duct pipe for the extractor hood be built into the wall or core drilled?

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Second option (core drilling), which is also a bit more expensive (about €150?), I personally find cleaner. But the first option is to fix the pipe in place first and then brick around it. The question is, if you do it that way, whether you can later attach backflow flaps or [Rostgitter]?

Why shouldn't that be possible?

For me, what the kitchen person said also sounds illogical. So far, we have decided on a different kitchen builder. He said both variants are possible, but with the second one you save about 200 €. That’s why I got a suitable pipe for it (telescopic pipe with a 162 mm diameter). Will a 150 one fit afterwards. My despair remains whether there will be enough space afterwards between the roof of the equipment room (behind the kitchen wall) and the roof overhang (bungalow)!