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Context. Since the discovery of exoplanetary systems, questions have been raised as to the sub-stellar companions that can survive encounters with their host star, and how this interaction may affect the internal structure and evolution of the hosting star, and particularly its surface chemical composition. Aims. We study whether the engulfment of a brown dwarf (BD) by a solar-like main-sequence (MS) star can significantly alter the structure of the star and the Li content on its surface. Methods. We performed 3D smoothed particle hydrodynamics simulations of the engulfment of a BD with masses 0.01 and 0.019 M ⊙ , on an MS star of 1 M ⊙ and solar composition, in three different scenarios: a head-on collision, a grazing collision with an impact parameter η  = 0.5  R ⊙ , and a merger. We studied the dynamics of the interaction in detail, and the relevance of the type of interaction and the mass of the BD on the final fate of the sub-stellar object and the host star in terms of mass loss of the system, angular momentum transfer, and changes in the Li abundance on the surface of the host star. Results. In all the studied scenarios, most of the BD mass is diluted in the denser region of the MS star. Only in the merger scenario a significant fraction (∼40%) of the BD material would remain in the outer layers. We find a clear increase in the surface rotational velocity of the host star after the interaction, ranging between 25 km s −1 (grazing collision) to 50 km s −1 (merger). We also find a significant mass loss from the system (in the range 10 −4  − 10 −3   M ⊙ ) due to the engulfment, which in the case of the merger may form a circumstellar disk-like structure. Assuming that neither the depth of the convective envelope of the host star nor its mass content are modified during the interaction, a small change in the surface Li abundance in the head-on and grazing collisions is found. However, in the merger we find large Li enhancements, by factors of 20 − 30, depending on the BD mass. Some of these features could be detected observationally in the host star, provided they remained for a long enough time. Conclusions. In our 3D simulations, a sizable fraction of the BD survives long enough to be mixed with the inner core of the MS star. This is at odds with previous suggestions based on 1D simulations. In some cases the final surface rotational velocity is very high, coupled with enough mass loss that may form a circumstellar disk. Merger scenarios tend to dilute considerably more BD material on the surface of the MS star, which could be detected as a Li-enhancement. The dynamic of the simulated scenarios suggests the development of asymmetries in the structure of the host star that can only be tackled with 3D codes, including the long-term evolution of the system.