 With the direct conversion of structures we want to obtain as a result the equivalence of validity in the original structures for \(\XL\), call them simply \(\Str(\XL)\), with validity of a certain class of many-sorted formulas (the translations) in the class \(\mathfrak{S}^{\ast}\) of converted structures (where \(\mathfrak{S}^{\ast}=\Conv_{1}(\Str(\XL))\)).