Both companies need their own authority. Although both companies may have the same owners and corporate officers, they are considered to be separate companies located in different countries. The Mexico-domiciled carrier needs an OP-2 application (for a commercial zone authority) unless they do not already have a US DOT number or other authority, in which case, they must register via the Unified Registration System. If they are a long-haul carrier that operates outside the commercial zone, they must fill out the OP-1(MX) application.
The U.S.-domiciled carrier or enterprise carrier must register for operating authority as well. For information on how to apply, click here. The motor carrier must pay the $300 application fee for each application.