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We apply the Barker-Henderson (BH) perturbation theory to the study of a Lennard-Jones fluid confined in a random porous matrix formed by hard sphere particles. In order to describe the reference system needed in this perturbation scheme, the extension of the scaled particle theory (SPT) is used. The recent progress in the development of SPT approach for a hard sphere fluid in a hard sphere matrix allows us to obtain very accurate results for thermodynamic properties in such a system. Hence, we combine the BH perturbation theory with the SPT approach to derive expressions for the chemical potential and the pressure of a confined fluid. Using the obtained expressions, the liquid-vapour phase diagrams of a LJ fluid in HS matrix are built from the phase equilibrium conditions. Therefore, the effect of matrix porosity and a size of matrix particles is considered. It is shown that a decrease of matrix porosity lowers both the critical temperature and the critical density, while the phase diagram becomes narrower. An increase of a size of matrix particles leads to an increase of the critical temperature. From the comparison it is observed that the results obtained from the theory are in agreement with computer simulations. The approach proposed in the present study can be extended to the case of anisotropic fluid particles in HS matrices.