  Given an open book decomposition (S,h) adapted to a closed, oriented
3-manifold M, we define a chain map from a certain Heegaard Floer chain complex
associated to (S,h) to a certain embedded contact homology chain complex
associated to (S,h), as defined in arXiv:1008.2734, and prove that it induces
an isomorphism on the level of homology. This implies the isomorphism between
the hat version of Heegaard Floer homology of -M and the hat version of
embedded contact homology of M.
