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This paper proposes using the unmanned aerial vehicle (UAV)-mounted intelligent reflecting surface (IRS) as a flying relay to enable the communication between the base station (BS) and suburb access points (APs). Since the UAV flight endurance is mainly affected by the weight of the IRS mounted on it, it is significant to reduce the IRS weight by minimizing the number of its reflecting elements. Regarding this, we propose an Optimized Phase Shift (OPS) algorithm to adjust the phase shift of the IRS reflecting elements, aiming to minimize the number of IRS reflecting elements required to successfully serve the APs while satisfying the signal-to-noise ratio (SNR) requirement.