Move a polygon to a different place on the globe, while maintaining its true geographical size? (QGIS)

I suggest you save as, the shape that you want to move as a new shapefile and move it however ever you want. However, have the original shapefile that is not moved. Having separate shapefiles allows you to maneuver the shape and save your edits without tampering with the original and correct dataset.

you should project your data into an equal area projection (e.g. cylindrical equal area, EPSG:9835). Then you can move your polygon to another place in order to illustrate the size difference. After saving your edit, you can project back to Mercator so that the shape of Africa (or your other country of interest) is the same.

You can achieve this visually in a Print Layout without manipulating your data.

1. Create two maps in print layout. Center one map on country 1, and the other map on country 2. Change the item Id of each map to the name of the country in that map.

   

2. Move the front map on top of the back map, and resize one of the map so they're the same size. Turn off the background for the front map. Set both maps to the same scale.

3. Set the CRS of both maps to an equal area projected coordinate system. Note that the scale of the map item may change when you change the CRS, so make sure to change it back so both maps are at the same scale.

   • Here's what Africa and Greenland look like with both maps in EPSG:54036 World_Cylindrical_Equal_Area.

     

   Looks terrible, right? That's because Greenland is really close to the North Pole, and Africa is centered on the Equator. They're never going to look good in the same projection.

4. In cases where the two countries are at very different latitudes, and/or one of them is close to a pole, they won't look "right" in the same projection. Change the CRS of each map to a projection centered on the country in that map. Ideally these would be similar types of projections, eg both Albers equal area conic. Unfortunately in the case of Greenland, the options are quite limited. Try out some different combinations, and see what you're happy with.

   • Here's what Greenland and Africa look like in EPSG:5938 WGS 84 / EPSG Greenland Polar Stereographic and EPSG:102022 Africa_Albers_Equal_Area_Conic, respectively:

     

   • Here's what Greenland and Africa look like with the Greenland map changed to EPSG: 3574 WGS 84 / North Pole LAEA Atlantic, and Africa still in Africa_Albers_Equal_Area_Conic:

     

You can move around the globe many countries here https://thetruesize.com/