  We show that the endomorphism ring of any nonzero finitely generated
projective module over the Leavitt path algebra $L_K(E)$ of an arbitrary graph
$E$ with coefficients in a field $K$ is isomorphic to a Steinberg algebra. This
yields in particular that every nonzero corner of the Leavitt path algebra of
an arbitrary graph is isomorphic to a Steinberg algebra. This in its turn gives
that every $K$-algebra with local units which is Morita equivalent to the
Leavitt path algebra of a row-countable graph is isomorphic to a Steinberg
algebra. Moreover, we prove that a corner by a projection of a $C^*$-algebra of
a countable graph is isomorphic to the $C^*$-algebra of an ample groupoid.
