How to transfer same Ship Method from Purchase Requisition -->Transfer Order --> Sales Order?

Is there any way we can ensure that the shipping method entered in a Purchase Requisition is passed to the Transfer Order and then from Transfer Order to a Sales Order?

Users are creating PR which in turn creates a TO and thereafter a SO (we have enrichment rules defined).

This is needed because user wants to ensure the same Ship Method gets sent to the Logical Service Provider to whom we send the Sales Order for Shipping.

Thanks,

Krishna