I would like to convert a shapefile which has
+ellps=WGS. In my understanding, even QGIS 1.8.0, it is impossible.
Let me know the free software which is able to convert shapefile from bessel to WGS.
It is very simple:
Load the shapefile into QGIS, right-click on the Layer ->
properties , general tab should contain
EPSG:4004 (or an EPSG code of some other CRS that is based on the bessel ellipsoid).
Then right-click again,
Format: ESRI Shapefile add a different file name CRS -> Select, EPSG:4326
QGIS can do that transformation but, to convert data which have coordinate systems with different ellipsoids, you have to have transformation parameters (+towgs for example) or know exact EPSG code of both data sources. Knowing only ellipsoid is not enough.