In the context of growing interest in strain engineering, we present a theoretical protocol for the reconstruction of extrinsic and intrinsic strain tensors in single-crystals attached to a template, with an arbitrary oriented coordinate system. Input data for the protocol are extrinsic deformations of lattice planes, i.e., measured with reference to a template. By combining the protocol with elasticity theory, material property modification can be elucidated. Different methods for strain measurements can take advantage of this approach. It has been applied for reconstruction of strain tensor depth distribution in off-axis LiTaO3 crystals implanted with H+ ions, which is the key step for piezoelectric thin film-on-insulator fabrication by the Smart Cut process. Modifications of composition, lattice parameters, and elastic constants are indicated and discussed