How to express the angular momentum in non inertial Earth frame like Earth Fixed frame so that angular momentum is conserved ?
Is H = R x mV still valid when R and V are taken in the rotating frame ?
Yes, $\vec H = \vec r \times (m \vec v)$ is still valid in a rotating frame. That's the definition, after all. Whether this definition has any meaning is a different question. Angular momentum is not necessarily conserved in a rotating frame. Consider, for example, a spacecraft in a geosynchronous orbit that has a non-zero inclination with respect to the equator and a non-zero eccentricity. The angular velocity vector as defined by $\vec r \times (m \vec v)$ points all over the place.