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I'd like to combine two layers of different administrative areas. One layer is more accurate (layer A) than the other one (layer B) in terms of generalization.

Is there a prepared QGIS-tool to do this?

It is essential that layer A is preserved in its shape. Due to the different degree of generalization the poylgons' boundarys will differ as you can see in the picture.

Layer A is red and transparent, layer B is green.

My first attempt was to substract layer A from B. By that it is ensured that at least the shape from the features of A are preservingly included. But close to the meeting edges from those two layers there happen to be fragments of the replaced features. I'd like those fragments not to be merged with the replaced ones, but merged with features they didn't originally belong to.

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I'm not sure if I understood correctly the second part of your question, but you can try the Difference tool and set Layer A as an overlay layer. This will preserve Layer A and change the geometry of Layer B so that the polygons become adjacent.

But if there are any gaps between polygons, this operation won't close them and you will have to do it manually by entering the edit mode, enabling snapping and editing the geometry of Layer B.

Alternatively, you can use the Snap geometries to layer tool, as suggested by csk. It is able to deal with gaps, but might be a little tricky to set up.

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