Inverse bone poser (blender 2.93)

import bpy
import math
import mathutils

active_object = bpy.context.active_object
other_object = None
all_armatures = True
sel_obj_count = 0
for o in bpy.context.selected_objects:
    sel_obj_count += 1
    if o.type != "ARMATURE":
        all_armatures = False
    else:
        if o != active_object:
            other_object = o

if sel_obj_count == 2 and all_armatures:

    bpy.ops.object.posemode_toggle()
    other_object_rest_bone_new_matrices = {}
    active_object_rest_bone_new_matrices = {}

    for active_object_pose_bone in active_object.pose.bones:
        other_object_rest_bone_new_matrices[active_object_pose_bone.name] = None
        active_object_rest_bone_new_matrices[active_object_pose_bone.name] = None

    bpy.ops.object.posemode_toggle()
    bpy.ops.object.editmode_toggle()

    for other_object_rest_bone_name in other_object_rest_bone_new_matrices:
        for rest_b in other_object.data.edit_bones:
            if rest_b.name == other_object_rest_bone_name:

                other_object_rest_parent_matrix = mathutils.Matrix.Identity(3)
                if rest_b.parent:
                    other_object_rest_parent_matrix = rest_b.parent.matrix.to_3x3()
                other_object_rest_matrix = rest_b.matrix.to_3x3()

                other_object_rest_bone_new_matrices[other_object_rest_bone_name] = (other_object_rest_parent_matrix.transposed() @ other_object_rest_matrix).to_4x4()
                break

    for active_object_rest_bone_name in active_object_rest_bone_new_matrices:
        for rest_b in active_object.data.edit_bones:
            if rest_b.name == active_object_rest_bone_name:

                active_object_rest_parent_matrix = mathutils.Matrix.Identity(3)
                if rest_b.parent:
                    active_object_rest_parent_matrix = rest_b.parent.matrix.to_3x3()
                active_object_rest_matrix = rest_b.matrix.to_3x3()

                active_object_rest_bone_new_matrices[active_object_rest_bone_name] = (active_object_rest_parent_matrix.transposed() @ active_object_rest_matrix).to_4x4()
                break

    bpy.ops.object.editmode_toggle()
    bpy.ops.object.posemode_toggle()

    for active_object_pose_bone in active_object.pose.bones:
        if active_object_pose_bone.name in active_object_rest_bone_new_matrices and active_object_pose_bone.parent:
            active_object_pose_bone.matrix_basis = other_object_rest_bone_new_matrices[active_object_pose_bone.name].transposed() @ active_object_rest_bone_new_matrices[active_object_pose_bone.name]
            active_object_pose_bone.matrix_basis = active_object_pose_bone.matrix_basis.transposed()

    bpy.ops.object.posemode_toggle()