What is the best way to make transformations between ellipsoids using PYPROJ?

[depicted-candela]

I am transforming coordinates between the Ellipsoids WGS84 and Hayford International using the code

>>> from pyproj import CRS, Transformer
>>> wgs84_crs = CRS.from_user_input("+proj=longlat +ellps=WGS84")
>>> hayford_crs = CRS.from_user_input("+proj=longlat +ellps=intl")
>>> transformer = Transformer.from_crs(wgs84_crs, hayford_crs, always_xy=True)
>>> wgs84_lon = -77.0369
>>> wgs84_lat = 38.9072
>>> hayford_lon, hayford_lat = transformer.transform(wgs84_lon, wgs84_lat)
>>> print(f"Hayford International coordinates (%5.2f, %5.2f): %5.2f, %5.2f" % (wgs84_lon, wgs84_lat, hayford_lon, hayford_lat))
Hayford International coordinates (-77.04, 38.91): -77.04, 38.91

The result is a change of zero between ellipsoid coordinates. The change is zero again with several random coordinates. How to make well this transformation?