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up to December last year I used the following command to convert Bavarian NAS data to shapefiles:

"C:\Program Files\QGIS 2.18\bin\ogr2ogr.exe" "ESRI Shapefile" -skipfailures -s_srs "+proj=tmerc +lat_0=0 +lon_0=12 +k=1 +x_0=500000 +y_0=0 +ellps=bessel +towgs84=598.1,73.7,418.2,0.202,0.045,-2.455,6.7 +units=m +no_defs" -t_srs EPSG:31468 NASdata.xml

The projection then was Gauss-Krueger. Since January 2019 the projection has changed to ETRS89 / UTM.

Now I wonder if it would be enough to simply replace the EPSG with "EPSG:25832" in the above command or is there anything else that must be replaced or added?

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You must also replace projection decription (parameter -s_srs) with description for EPSG:25832 (see https://epsg.io/25832):

-s_srs "+proj=utm +zone=32 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs"

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