  This paper is the second in a series of three, the aim of which is to
construct algebraic geometry over a free metabelian Lie algebra $F$. For the
universal closure of free metabelian Lie algebra of finite rank $r \ge 2$ over
a finite field $k$ we find a convenient set of axioms in the language of Lie
algebras $L$ and the language $L_{F}$ enriched by constants from $F$. We give a
description of:
  * The structure of finitely generated algebras from the universal closure of
$F_r$ in both $L$ and $L_{F_r}$
  * The structure of irreducible algebraic sets over $F_r $ and respective
coordinate algebras.
  We also prove that the universal theory of a free metabelian Lie algebra over
a finite field is decidable in both languages.
