I would be very surprised if anyone has published such a map - it would be a cartographic nightmare, with almost no useful properties (it would be neither conformal nor equal area). It would be interesting to know the application - it may be that something else would be more suitable. However, it would be relatively straightforward to produce one in almost any GIS package, and the data for world maps are freely available. I suggest that you point him in the direction of the geography or GIS department of his local university. Otherwise, the web-site http://www.remotesensing.org/packages/index.php may be of help - it has free packages for plotting maps, and is the source for the best projection package available (proj).
Paul Cooper, who maps the opposite pole!