I used to have to do this...you could cut and paste a raster image of the Google Earth data by print screen or whatever you like. But, have you tried using the Bing Maps layer provided by ESRI this would make it much easier as you have imagery just as good as Google Earth within the ArcMap interface...
Otherwise if you have been making KMZ files in Google Earth have you had a look at importing them into ArcGIS (I am not sure if you can).
Where can I find that bing map layer? Does is cover South Africa? i.t.o. the google images: Mapwindow GIS is open source freeware with a nice little plugin to import a screenshot of GE together with the projection.it's called shape2earth. only con is it's restricted to your screen resolution.
plz let me know if you find a tool that can import high quality images
Additionally you could download GoogleEarth Pro which I think is relatively expensive where you can import and export shapefiles between the two programmes but I am not sure of imagery.
However being able to export your shapefiles into kmz/kml file format means you can overlay this on imagery.
I would also point out that within ArcGIS Toolbox (using ArcGIS10) there is a conversion tool to KML (which opens in Google) look for Conversion Tools>To KML and pick your tool (this has also worked for me in the past).
i am having a tool,with that its possibly to download the Google earth images with lat long values. i downloaded 350 sqm area images with high quality.