  The monogenic free inverse semigroup $FI_1$ is not finitely presented as a
semigroup due to the classic result by Schein (1975). We extend this result and
prove that a finitely generated subsemigroup of $FI_1$ is finitely presented if
and only if it contains only finitely many idempotents. As a consequence, we
derive that an inverse subsemigroup of $FI_1$ is finitely presented as a
semigroup if and only if it is a finite semilattice.
