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An accretion disc can be formed around a secondary non-evolved star in a binary system when the primary companion leaves the Main sequence and starts to lose mass with an enhanced rate due to slow stellar wind. We analyze accretion disc evolution and planetary migration in such discs around solar-like Main sequence stars in binary systems with evolved companions. A disc is formed from the stellar wind matter and its properties depend on the mass loss rate by the donor and the binary’s parameters. We use a numerical model to study non-stationary discs with mass inflow on the whole disc surface within the Bondi radius during late stages of the primary evolution. Then, the migration path of a single planet embedded in such a non-stationary disc is determined by the migration rate varying in the course of the disc evolution. In binary systems with initial separation $a\lesssim 80$~--~100 AU giant planets efficiently migrate in such discs and typically approach short distances from the host star where tidal forces become non-negligible. Neptune-like planets can reach these internal parts of the system in cases when a donor is a relatively massive star (5-8 M$_\odot$) or in binaries with $a \lesssim 20$~AU. We conclude that in binaries, mass loss from the primary component at late evolutionary stages can significantly modify structure of a planetary system around the non-evolved secondary component, probably resulting in mergers of massive planets with the host star.