  In the previous article "Hearts of twin cotorsion pairs on exact categories",
we introduced the notion of the heart for any cotorsion pair on an exact
category with enough projectives and injectives, and showed that it is an
abelian category. In this paper, we construct a half exact functor from the
exact category to the heart. This is analog of the construction of Abe and
Nakaoka for triangulated categories. We will also use this half exact functor
to find out a sufficient condition when two different hearts are equivalent.
