  In this paper we continue the description of solvable Leibniz algebras whose
nilradical is a filiform algebra. In fact, solvable Leibniz algebras whose
nilradical is a naturally graded filiform Leibniz algebra are described in
\cite{Campo} and \cite{SolGFil}. Here we extend the description to solvable
Leibniz algebras whose nilradical is a filiform algebra. We establish that
solvable Leibniz algebras with filiform Lie nilradical are Lie algebras.
