Decide transform via one-to-one mapping

You are given two strings s and t of equal length over the lowercase English alphabet. In one step, you may pick any character x and replace all its occurrences in s with a single character y (the mapping x→y must be applied consistently across the entire string and persists for subsequent steps). Determine whether s can be transformed into t in finitely many steps. If cycles occur in the mapping, you may only break them if there exists at least one spare character not present in t to use as a temporary buffer. Design an algorithm to decide transformability and, if possible, output one valid sequence of replacements.