For technical applications, it is important to be able to solve the radiation transport equation under reflection conditions rather than under free boundary conditions. The reflection conditions lead to the situation when all angular directions for which the transport equation is calculated are dependent on each other even in the case of the absence of scattering. The angular directions are taken from a discrete set of nodes of the cubature formula on the unit sphere and the implementation of reflection conditions leads to the necessity of remaining within this discrete set of angular directions. One of the variants of the algorithm, based on the implementation of a discrete analogue of the radiation flux conservation at the boundary, is presented in this paper. The use of the interpolation-characteristic scheme entails the need to construct the correct reflection condition not only on faces, where it is simple, but also on vertices and edges, where it requires additional definitions due to the lack of the concept of normal. The radiation density as an integral value depends not only on the scheme error of the solution of the transport equation but also on the error of the cubature formulas used. For smooth solutions (as there are usually quite a small number of nodes on the sphere) the effect of errors in cubature formulas is small. In the case of an undifferentiated solution, there is a threshold value for the fineness of the partitioning of the spatial grid so that, at steps below this value, the error of the cubature formula makes the main contribution to the error.