  The paper is devoted to classification problem of finite dimensional complex
none Lie filiform Leibniz algebras. Actually, the observations show there are
two resources to get classification of filiform Leibniz algebras. The first of
them is naturally graded none Lie filiform Leibniz algebras and the another one
is naturally graded filiform Lie algebras. Using the first resource we get two
disjoint classes of filiform Leibniz algebras. The present paper deals with the
second of the above two classes, the first class has been considered in our
previous paper. The algebraic classification here means to specify the
representatives of the orbits, whereas the geometric classification is the
problem of finding generic structural constants in the sense of algebraic
geometry. Our main effort in this paper is the algebraic classification. We
suggest here an algebraic method based on invariants. Utilizing this method for
any given low dimensional case all filiform Leibniz algebras can be classified.
Moreover, the results can be used for geometric classification of orbits of
such algebras.
