The Earth's albedo is the fraction of short-wave solar radiation that is reflected back to space, and is key to understand the observed trends in climate change. Although there have been many observational approaches to estimate the Earth's albedo, different methods have their own drawbacks, for example, artificial satellites have a finite life time, and are operating in a hard environment that could quickly degrade the detectors. The Moon, the only natural satellite of Earth, offers an additional platform for monitoring the Earth's albedo. In this paper, we calculate the global TOA (top-of-atmosphere) albedo that would be observed by a theoretical observatory on the Moon, and compare it with long-term trends derived from CERES (Clouds and the Earth's Radiant Energy System, 2000-2020) and earthshine data (1999-2017). We find that the global hourly mean albedo observed in the direction of the Moon is more variable because of the orbital movement of the Moon. However, the regional and long-term global mean albedo anomalies that would be observed by CERES and has a good general agreement by a lunar observer over 20 years the data spans. Similarly, earthshine data show a steady decline during two decades of about 0.7 W /m2 which is in line with the decline of 0.5 W /m2 that would be observed from the Moon. Besides, to compare the regional changes of albedo with CERES, the spatially-resolved decadal anomalies in the albedo are also calculated for analysis. We find that a lunar-based observatory would be capable of detecting similar changes seen from CERES. Thus, it is a a practical option to monitor the long-term trends in albedo from the point of view of capturing the variability in the TOA fluxes of the Earth's atmosphere.