Generate skinned mesh in runtime

I want to create a script that loads character head from an external source.

I already have a character without a head, and it sits comfortably in the origin as shown here: Everything works as I expect, including animations.

Then I load mesh data from external source and add it to scene using the following code:

         var character = GameObject.Find ("fuse_base_character");
 
         var headObject = new GameObject ("head");
         headObject.AddComponent<SkinnedMeshRenderer> ();
         headObject.transform.SetParent (character.transform);
 
         var headRenderer = headObject.GetComponent <SkinnedMeshRenderer> ();
         headRenderer.sharedMesh = mesh;
         var rig = GameObject.Find ("mixamorig:Hips");
         headRenderer.rootBone = rig.transform;

Head is in exactly the same coordinate frame as the body, I can confirm that by opening both models in a 3D editor. But when I execute this code, head appears far higher than it should:

Head has exactly the same "armature" as the body, so even animations work. But head flies 3 meters above the ground instead of being in it's proper place.

I found that this happens because head uses position of the root bone as it's origin, instead of world origin! Thus it appears shifted relative to the rest of the body, because body uses world origin.

I tried to headObject.transform.Translate and headRenderer.transform.Translate, but this does not change anything. How should I add this mesh to the scene so it uses correct coordinate system? Please excuse me if the question is dumb, I am very new to Unity!