Englishal. There's a list of six "approved" schools in message one, and a comment from yourself in message five saying;
The way some of these companies work is train a student for an FAA PPL.
I challenge you to tell us exactly which one(s) of these schools train for FAA and then do a conversion test....or retract the statement.
AFAIK, the conversion skill test "does" have to be carried out at an approved organisation - although I would be very happy to be corrected or proven wrong on that one.