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Considered is the problem of electromagnetic wave radiation and absorption in the presence of a two-layer lossy dielectric sphere partially covered with a metal screen and illuminated by an elementary electric dipole. To find the field, the authors expand it in terms of spherical functions and use the method of analytical regularisation to reduce the problem to a matrix equation with favourable features. This enables us to obtain the radiation and absorption characteristics in a wide range of parameter variations and compare the efficiencies of shielding by different screens of varying angular size. As the studied structure can be viewed as a model of a head phantom with a helmet, the presented analysis can be useful for a control of specific microwave absorption rate levels.