The present invention refers to the method for synthesis an absorbent material consisting of a phase of tetravalent manganese feroxyhyte (δ-Fe(1-x)MnxOOH) with a negatively charged grain surface in which a percentage of iron has been isomorphically substituted by manganese atoms at 0.05-25%. Its' production is carried out in two continuous flow stirred-tank reactors arranged in serial configuration, where mild acidic conditions (pH 5-6) prevail in the first reactor and mild alkaline conditions (pH 9-10) together with high redox potential (600-700 mV) in the second reactor. The material can be used to uptake mercury, as well as other heavy metals from both water and hot gas streams. Specifically, the adsorption capacity is determined by the magnitude of the negative surface charge and the isoelectric point that can be both adjusted by the synthesis process parameters.