The high-penetration path loss and distance are the major limiting factors of the millimeter wave (mmWave) technology. It consequently requires a line-of-sight environment to accommodate the source and destination nodes, while the presence of in-between obstacles becomes inevitable due to the ever-increasing densification of modern wireless networks. Nonorthogonal multiple access (NOMA) and fluid antenna system (FAS) can play important roles in expanding the range of communication. We propose an N-user NOMA network that utilizes the base station's resources efficiently and implements cooperative full-duplex communication. Furthermore, the considered L-port FAS technique improves the quality-of-service by designing a flexible and low-profile antenna for mobile users. Simulation results reveal that 10-port FAS outperforms the selection combining technique while requiring around 600 ports to beat the performance of a four-antenna maximum-ratio-combining scheme. Finally, we formulate the outage probability expressions considering residual self-interference and interference, which are validated through Monte Carlo simulations.