This paper studies the two-stage no-wait hybrid flow shop scheduling problem with a single server at the first stage, involving two parallel machines in stage one and a single machine in stage two. The presence of no-wait and server constraints makes the problem highly challenging. A mixed-integer programming (MIP) model is proposed to solve small instances optimally. For larger cases, we develop two constructive heuristics and metaheuristic approaches, including SA and several variants of GVNS. Computational experiments show that while the MIP is limited to small sizes, GVNS significantly outperforms the heuristics and SA, delivering high-quality solutions in short computation times. The best GVNS variant achieves the lowest average gaps relative to the lower bound, demonstrating the efficiency and robustness of the proposed methods.