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Embedded fiber Bragg gratings can be subjected to arbitrary states of strain including shear strain. Such perturbations can cause coupling between polarization modes. Coupled-mode theory in Bragg gratings so far neglected this effect and only considered forward-backward coupling. Polarization mode coupling within a Bragg grating leads to interdependencies between Bragg reflection peaks which have so far been unaddressed. We formulate a full strain tensor treatment of fiber Bragg gratings, considering the coupling of the polarization modes within the grating. We give an approximation for the coupling coefficients affecting the polarization mode coupling and numerically solve the coupled-mode equations for representative states of strain. We show in which way shear strain affects the optical response of a grating and demonstrate how the fiber's beat length influences this characteristic.