For a change (really) I agree with bose-x here.
And unfortunately a letter from the Atlanta FSDO from 5 years ago may not hold up with the local FSDO as they have the authority to interpret things differently. These sorts of things are useless unless you have a letter of authorization from the local FSDO that has jurisdiction over the school in question.
Anyways, back to the original questions.
Back in the day you used to be able to get a FAA CPL based on your foreign license. But..it would read "not valid for Commercial operations"
As of the 1980-ies they do not issue anything but a PPL based on foreign license. This can be done by a UK based examiner if he filed the paperwork with the FAA to get the authorization.
Which means you will have to fly the plane in question under PPL privileges...whatever you understand that to be.