GDAL does not recognize EPSG code of a shapefilefile reprojected by ogr2ogr

I am using ogr2ogr to reproject shapefiles. For example:

ogr2ogr -s_srs EPSG:1234 -t_srs EPSG:3857 dest.shp srs.shp

ogr2ogr then creates dest.shp, dest.shx, dest.dbf and dest.prj as expected.

The problem occurs when I try to find the EPSG code of dest.shp using GDAL. GDAL cannot identify that the file is in EPSG 3857.

Why can't GDAL identify a prj's EPSG when it created the prj from a EPSG?

Please note that I am using GDAL C# library.