This is a matter that should be resolved by Supplier B since they are ultimately responsible for compliance with the International Traffic in Arms Regulations.  Based on experience with industry, here are three potential courses of action (easiest to hardest) in my experience:

1) Supplier B either finds a way to resolve the AES filing issue through a solution other than a Power of Attorney  with the current Freight Forwarder or hires another Freight Forwarder that will be willing to use the Supplier A ISO DSP-5 as a basis for the AES filing.

2) Supplier B could add Supplier A as a party (authorized user) to their MLA through an amendment authorized by the State Department Directorate of Defense Trade Controls (DDTC).

3) Supplier A could seek a DDTC General Correspondence Letter advising both U.S. Customs and Border Protection (CBP) and Supplier B to use the Supplier A ISO DSP-5 as the basis for the AES filing.

Ultimately, however, it's up to Supplier B to orchestrate a resolution to this situation that is acceptable to both Supplier A and the USG (DDTC and CBP).