Hello Probert,
good holiday!
When you export from ArcGis, check your prj file. It should have an AUTHORITY["EPSG","9518"] record in case of WGS84 + EGM2008 compound CS as in:
COMPD_CS["WGS 84 + EGM2008 height",
GEOGCS["WGS 84",
DATUM["World Geodetic System 1984 ensemble",
SPHEROID["WGS 84",6378137,298.257223563,AUTHORITY["EPSG","7030"]],TOWGS84[0,0,0,0,0,0,0],AUTHORITY["EPSG","6326"]],
PRIMEM["Greenwich",0,AUTHORITY["EPSG","8901"]],
UNIT["degree",0.01745329251994328,AUTHORITY["EPSG","9102"]],AUTHORITY["EPSG","4326"]],
VERT_CS["EGM2008 height",
VERT_DATUM["EGM2008 geoid",2005,AUTHORITY["EPSG","1027"]],
UNIT["metre",1,AUTHORITY["EPSG","9001"]],AUTHORITY["EPSG","3855"]],
AUTHORITY["EPSG","9518"]]
if not present then MS will not recognize the CS and better to just delete the prj and during import specify the correct CS...
Hope this is helpful