Intelligent reflecting surface (IRS) is a promising technology to deliver the higher spectral and energy requirements in fifth-generation (5G) and beyond wireless networks while shaping the propagation environment. Such a design can be further enhanced with massive multiple-input-multiple-output (mMIMO) characteristics towards boosting the network performance. However, channel reciprocity, assumed in 5G systems such as mMIMO, appears to be questioned in practice by recent studies on IRS. Hence, contrary to previous works, we consider frequency division duplexing (FDD) to study the performance of an IRS-assisted mMIMO system. However, FDD is not suitable for large number of antennas architectures. For this reason we employ the joint spatial division and multiplexing (JSDM) approach exploiting the structure of the correlation of the channel vectors to reduce the channel state information (CSI) uplink feedback, and thus, allowing the use even of a large number of antennas at the base station. JSDM entails dual-structured precoding and clustering the user equipments (UEs) with the same covariance matrix into groups. Specifically, we derive the sum spectral efficiency (SE) based on statistical CSI in terms of large-scale statistics by using the deterministic equivalent (DE) analysis while accounting for correlated Rayleigh fading. Subsequently, we formulate the optimization problem concerning the sum SE with respect to the reflecting beamforming matrix (RBM) and the total transmit power, which can be performed at every several coherence intervals by taking advantage of the slow-time variation of the large-scale statistics. This notable property contributes further to the decrease of the feedback overhead.