We have made a calculation of the propagation of positrons from dark-matter particle annihilation in the Galactic halo in different models of the dark matter halo distribution using our 3D code, and present fits to our numerical propagation Green's functions. We show that the Green's functions are not very sensitive to the dark matter distribution for the same local dark matter energy density. We compare our predictions with computed cosmic ray positron spectra ("background") for the

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... al" CR nucleon spectrum which matches the local measurements, and a modified spectrum which respects the limits imposed by measurements of diffuse Galactic gamma-rays, antiprotons, and positrons. We conclude that significant detection of a dark matter signal requires favourable conditions and precise measurements unless the dark matter is clumpy which would produce a stronger signal. Although our conclusion qualitatively agrees with that of previous authors, it is based on a more realistic model of particle propagation and thus reduces the scope for future speculations. Reliable background evaluation requires new accurate positron measurements and further developments in modelling production and propagation of cosmic ray species in the Galaxy.