This paper explores the implications of F-term hybrid inflation (FHI) in a $B-L$ extension of the Minimal Supersymmetric Standard Model (MSSM), focusing on SUSY breaking and cosmic string formation. The model respects a global $U(1)$ $R$ symmetry, with the hidden sector Kähler manifold having an enhanced $SU(1,1)/U(1)$ symmetry. The scalar curvature is determined by achieving a SUSY-breaking de Sitter vacuum without fine-tuning. FHI is consistent with data if the soft tadpole term magnitude is within $(1.2-100)$ TeV, and it is accompanied by the production of metastable $B-L$ cosmic strings. These strings, if metastable, can explain the observed stochastic gravitational wave background from pulsar timing array experiments, with a dimensionless tension $G\mu_{\text{CS}} \simeq (1-9.2) \cdot 10^{-8}$. The $\mu$ parameter of MSSM is generated through the Giudice-Masiero mechanism, facilitating out-of-equilibrium decay of the $R$ saxion at a reheat temperature below about 71 GeV. The prolonged matter-dominated era suppresses the gravitational wave signal at high frequencies. The SUSY mass scale is found to lie in the PeV region.This paper explores the implications of F-term hybrid inflation (FHI) in a $B-L$ extension of the Minimal Supersymmetric Standard Model (MSSM), focusing on SUSY breaking and cosmic string formation. The model respects a global $U(1)$ $R$ symmetry, with the hidden sector Kähler manifold having an enhanced $SU(1,1)/U(1)$ symmetry. The scalar curvature is determined by achieving a SUSY-breaking de Sitter vacuum without fine-tuning. FHI is consistent with data if the soft tadpole term magnitude is within $(1.2-100)$ TeV, and it is accompanied by the production of metastable $B-L$ cosmic strings. These strings, if metastable, can explain the observed stochastic gravitational wave background from pulsar timing array experiments, with a dimensionless tension $G\mu_{\text{CS}} \simeq (1-9.2) \cdot 10^{-8}$. The $\mu$ parameter of MSSM is generated through the Giudice-Masiero mechanism, facilitating out-of-equilibrium decay of the $R$ saxion at a reheat temperature below about 71 GeV. The prolonged matter-dominated era suppresses the gravitational wave signal at high frequencies. The SUSY mass scale is found to lie in the PeV region.