We propose a model, which describes the transfer of a marker inside the lymphatic microvessel by the lymph flow as a consequence of the vessel’s elastic deformation, which produces the pushing pressure jump. The resulting model is close to the equation of the nonlinear diffusion with a localized moving front solution. The simulations are compared with the processed data of experimental recordings of the transfer of neutrophil in the meningeal lymphatic capillary of Danio rerio, and the quantitative reproducing the realistic spatiotemporal dynamics is confirmed.