On the definition of suitable orderings to generate adjunctions over an unstructured codomain

Given a mapping f:A→B from a (pre-)ordered set A into an unstructured set B, we study the problem of defining a suitable (pre-)ordering relation on B   such that there exists a mapping g:B→A such that the pair of mappings (f,g)(f,g) forms an adjunction between (pre-)ordered sets. The necessary and sufficient conditions obtained are then expressed in terms of closure operators and closure systems.