Hello Ulrich,
Do you have the possibility in ArcGIS to specify, which channels should be used as Red, Green and Blue?
As a workaround, you can export the orthomosaic in False Colors representation, but it would lead to conversion to 8-bit RGB. In case it is not a problem for you, then you need to create three output channels in Raster Calculator dialog, set formulas as B1 / 65535, B2 / 65535 and B3 / 65535 (you can use smaller ration value in order to make the output brighter, but the same for all bands), in the Palette tab of Raster Calculator dialog select False Colors options and during the export enable Raster Transform -> Palette option.