Note a meaning shift. Cf. māˀu ‘excrement’ [CAD m1 435].
J. Huehnergard takes the presence of h- in MSA (and Hadramitic) at face value and reconstructs the prototype of the Akk. preposition as *ha-nā. However, the presence of *h- in proto-Akkadian is excluded by the Sargonic spelling a-na (Hasselbach 2005:167, Archi 2002:4) (Kogan 2015:119-120, 556).