The study of water masers at cosmological distances would allow us to investigate the parsec-scale environment around powerful radio sources, to probe the physical conditions of the molecular gas in the inner parsecs of quasars, and to estimate their nuclear engine masses in the early universe. To derive this information, the nature of the maser source, jet or disk-maser, needs to be assessed through a detailed investigation of the observational characteristics of the line emission. We monitored the maser line in the lensed quasar MGJ0414+0534 at z = 2.64 with the 300-m Arecibo telescope for ~15 months to detect possible additional maser components and to measure a potential velocity drift of the lines. In addition, we follow the maser and continuum emissions to reveal significant variations in their flux density and to determine correlation or time-lag, if any, between them. The main maser line profile is complex and can be resolved into a number of broad features with line widths of 30-160 km/s. A new maser component was tentatively detected in October 2008 that is redshifted by 470 km/s w.r.t the systemic velocity of the quasar. The line width of the main maser feature increased by a factor of two between the Effelsberg and EVLA observations reported by Impellizzeri et al. (2008) and the first epoch of the Arecibo monitoring campaign. After correcting for the lens magnification, we find that the total H2O isotropic luminosity of the maser in MGJ0414+0534 is now ~30,000 Lsun, making this source the most luminous ever discovered.[Abridged]
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