An FI(A) is a flight instructor (aeroplanes) as opposed to FI(H) for hicopleters. The FI(R) is really an FI(A)(R) or an FI(H)(R) the (R) is for Restricted. On first qualification as an instructor you are restricted in your authority - you have to be supervised and you can't send some solos. It's probably all on the CAA SRG web site somewhere.