The old System 34 is still being used in Denmark even though authorities changed to UTM/ETRS89. We regularly get files, especially when asking for information about local underground cables. Can anyone recommend a free tool/programm which can transform DXF/DWG or shapefiles in S34 to another - in QGIS usable - coordinate system?
OSGeo4W includes a recent release candidate of PROJ 5.0.0. The final release will soon be available as well.
The init files and grids linked to above is also included in the new proj-datumgrid-europe package that can be downloaded from proj4.org.
The real reason for QGIS not including System 34 is that no transformation library other than TrLib from the Danish geodetic office. That has now changed but, but actually using System 34 in QGIS requires that the new API is used. As far as I understand the QGIS developers are seeking to do that in the near future (probably release 3.2 or 3.4).
The new Proj version 5.0.0 adds support for nordic coordinate conversion, including S34. See https://github.com/NordicGeodesy/NordicTransformations for details.
There are no binaries yet for Windows except a release candidate, so you have to be patient for the implementation in GDAL and QGIS; or compile it yourself.
A possible reason for the exclusion of S34 in QGIS can be found in Clifford J. Mugnier's report on Denmark. They used a special "Buchwaldt" projection not used elsewhere.
See http://osgeo-org.1560.x6.nabble.com/Custom-projection-wildly-inaccurate-td3848728.html for further discussion.
Just to be sure: You're talking about this CRS?
If so, simply download the .proj-file from the link, add it to the folder of your shp, rename it to your shp-name and you should be able to open the file in QGis without problems. Then right-click the layer and use "save as" with your desired CRS.