If you form a corporation and that corporation manufactures (form 1) or purchases and transfers (form 4) that weapon than any member of the corporation that is listed as an allowable officer of said corporation may use the gun. This person should have a photocopy of the Form 1 or Form 4 and paperwork showing that they are an authorized officer of the corporation that owns the weapon.
Otherwise, no. For anyone to use a 1934 NFA gun, that your name is on the paperwork, you have to be present with them. If you loan an NFA gun to someone, and they take the gun out of your presence, they are in illegal posession of a gun that will send them to the Federal Bureau of Prisons for one or two decades.