This paper explores F-term hybrid inflation (FHI) in the context of a B-L extension of the Minimal Supersymmetric Standard Model (MSSM), with a focus on SUSY breaking and cosmic string (CS) production. The model is built on a global U(1) R symmetry, with the hidden sector's Kähler manifold enjoying an enhanced SU(1,1)/U(1) symmetry. The scalar curvature is determined by the achievement of a SUSY-breaking de Sitter vacuum without fine-tuning. FHI is consistent with data if the magnitude of the emergent soft tadpole term is in the range (1.2-100) TeV, and it is accompanied by the production of B-L cosmic strings. These strings, if metastable, can explain the observed stochastic gravitational wave background from PTA experiments with a dimensionless tension Gμ_cs ≈ (1-9.2) × 10⁻⁸. The μ parameter of MSSM is generated via the Giudice-Masiero mechanism, facilitating the out-of-equilibrium decay of the R saxion at a reheating temperature below ~71 GeV. The prolonged matter-dominated era suppresses the gravitational wave signal at high frequencies. The SUSY mass scale is predicted to lie in the PeV region, consistent with the Higgs boson mass observed at the LHC. The model also addresses the dark energy problem by tuning the SUSY-breaking superpotential parameter to a value of order 10⁻¹². The paper presents the complete particle content, the generation of neutrino masses, and the GWs from CS decay. It concludes that the model provides a viable framework for FHI, with predictions for the SUSY mass scale and the cosmic string tension.This paper explores F-term hybrid inflation (FHI) in the context of a B-L extension of the Minimal Supersymmetric Standard Model (MSSM), with a focus on SUSY breaking and cosmic string (CS) production. The model is built on a global U(1) R symmetry, with the hidden sector's Kähler manifold enjoying an enhanced SU(1,1)/U(1) symmetry. The scalar curvature is determined by the achievement of a SUSY-breaking de Sitter vacuum without fine-tuning. FHI is consistent with data if the magnitude of the emergent soft tadpole term is in the range (1.2-100) TeV, and it is accompanied by the production of B-L cosmic strings. These strings, if metastable, can explain the observed stochastic gravitational wave background from PTA experiments with a dimensionless tension Gμ_cs ≈ (1-9.2) × 10⁻⁸. The μ parameter of MSSM is generated via the Giudice-Masiero mechanism, facilitating the out-of-equilibrium decay of the R saxion at a reheating temperature below ~71 GeV. The prolonged matter-dominated era suppresses the gravitational wave signal at high frequencies. The SUSY mass scale is predicted to lie in the PeV region, consistent with the Higgs boson mass observed at the LHC. The model also addresses the dark energy problem by tuning the SUSY-breaking superpotential parameter to a value of order 10⁻¹². The paper presents the complete particle content, the generation of neutrino masses, and the GWs from CS decay. It concludes that the model provides a viable framework for FHI, with predictions for the SUSY mass scale and the cosmic string tension.