At a top level the FMS Case(s) related to contract that the DoD contractor is performing should have a Transportation Plan (TP) per eSAMM Chapter 7.

We also consulted with our Defense Security Cooperation University (DSCU) colleages, who offered some add'l thoughts based on their interpretation of the question.  If the "controlled" material includes Controlled Cryptographic Items (CCI), the specific eSAMM policies that apply are SAMM C7.15.4 (Controlled Cryptographic Items (CCI)) which includes numerous pertinent transportation policies including the statement, "All deliveries of CCI require the transfer of the item from the appropriate COMSEC Custodian in the United States Government (USG) to the purchaser's COMSEC Custodian."  SAMM C7.13 (Transportation Plan) also includes the following guidance; "A Transportation Plan is required for each Letter of Offer and Acceptance (LOA) containing Classified (CONFIDENTIAL and SECRET), Sensitive, including Controlled Cryptographic Items (CCI), or Arms, Ammunition, & Explosives (Security Risk Categories I - IV).  The plan covers all movement including final receipt by the Designated Government Representative (DGR) or other designated representative acting for the DGR."

Accordingly, the DoD contractor should contact Contracting Officer (or Contracting Officer Rep) to determine what the FMS Case Transportation Plan says re: handling and shipment any/all relevant "controlled items" pertaining to their contract.  The DoD contractor should follow the TP guidance the CO or COR provide, which would typically be obtained fom the applicable DoD Component FMS Implementing Agency's FMS Case Manager .