Occurrence
Vector objects such as Lines, Polylines or Polygons have been digitised into the incorrect projection. In this case, reprojection does not work, as the object coordinates will change (move). For
example the vector object may have been created in the incorrect UTM Zone, or the wrong projection was selected during import and registration of the file.
How can this be modified without recreating the objects/registration?
Solution
For vector data you can use this tool that you can install by going to Home>MapInfo Marketplace, and find CoordsysChanger and install it.
http://mapinfomarketplace.precisely.com/product/4d68d42c-7d5a-40c8-ab37-56c005176049
For rasters or surface grid images, simply use Table>Raster>Modify Image Registration, and select a new Projection, or edit control points. Note that editing control points may cause errors, which ought to be fixed through rectification.
For points, you can firstly save the coordinates using DISCOVER>Projections>Updates Coordinates. Then simply delete the map, using Table>Maintenance>Table Structure and un-ticking Table is Mappable, and then re-create the points.