The spin absorption process in a ferromagnetic material depends on the spin orientation relatively to the magnetization. Using a ferromagnet to absorb the pure spin current created within a lateral spin-valve, we evidence and quantify a sizeable orientation dependence of the spin absorption in Co, CoFe and NiFe. These experiments allow determining the spin-mixing conductance, an elusive but fundamental parameter of the spin-dependent transport. We show that the obtained values cannot be understood within a model considering only the Larmor, transverse decoherence and spin diffusion lengths, and rather suggest that the spin-mixing conductance is actually limited by the Sharvin conductance.