Try the import in both ILWIS 3.7.x and ILWIS 3.8.4. In the newer
version, the Shapefile import has been replaced by GDAL/OGR, so the
outcome that didn't work in once case, should work without problems in
the other. Inform me about your findings.
If it still doesn't import as-expected, please zip the Shapefile (the
files .shp, .shx, .dbf and the .prj if it is there), so that I can have
a look at it.