Yes, no magic button, fordmar, but for flat objects, that is sometimes an option inside the Cloner.
Not that I use it often, as I love UV data, which means stable and manually adjustable
https://help.maxon.net/c4d/2023/en-us/Default.htm#html/OMOGRAPH_CLONER-ID_OBJECTPROPERTIES.html#MGCLONER_FIX_TEXTURE
You mentioned the Pose Morph Tag; as this one produces the information for the Cloner, it needs to be above the Cloner in the Object Manager—processing order/Priorities, etc.
Enjoy