code: def _trace_S(s, j, b, S_cosets):
      """
      Return the representative h satisfying s[h[b]] == j
  
      If there is not such a representative return None
      """
      for h in S_cosets[b]:
          if s[h[b]] == j:
              return h
      return None
  
imports: from sympy.combinatorics.permutations import Permutation, _af_rmul, _af_invert, _af_new
  from sympy.combinatorics.perm_groups import PermutationGroup, _orbit, _orbit_transversal
  from sympy.combinatorics.util import _distribute_gens_by_base, _orbits_transversals_from_bsgs
label_desc: Use image node_id 3 for calling a global function with example usage: _trace_S(s, j, b, S_cosets) and returns: None, h