In Husserl's theory, 'Pairing' (Paarung) is the second phase of constitution of the other.
The other's body appears in my perceptual field, originally as objective and material. But it is constituted as a living body through analogy, that is, it is apprehended as an animate organism since it is similar to my own living body. The other's body is recognized as 'the other person's living body', paired to my own living body. There is a process of 'Pairing' of my body and that of the other. Husserl says:
...pairing first comes about when the Other enters my field of perception. I, as the primordial psychophysical Ego, am always prominent in my primordial field of perception, regardless of whether I pay attention to myself and turn toward myself with some activity or other. In particular, my live body is always there and sensuously prominent; but, in addition to that and likewise with primordial originariness, it is equipped with the specific sense of an animate organism. Now in case there presents itself, as outstanding in my primordial sphere, a body "similar" to mine --- that is to say, a body with determinations such that it must enter into a phenomenal pairing with mine --- it seems clear without more ado that, with the transfer of sense, this body must forthwith appropriate from mine the sense: animate organism.
[Husserl, E (1950/1988). Cartesian Meditation. (trans.) D. Cairns. London: Kluwer Academic. p.113]
In this passage, Husserl is simply claiming that I recognize the other's body as living body (Leib) because it is similar to mine. But how is the range of similarity asked here? For example, how about an animal's body?, a doll?, a robot? Do they have the body which can be paired to mine?
Anyway, what is important here is that we recognize the other person as an embodied being, before we recognize them as a mental being. The problem of other minds should be grounded on the embodiment.