LDT,
As Colban says, the three letter code on the front RHS of the gearbox will tell you about it.
Here is a link to a page that gives more detail (scroll down towards the bottom). The information has been gathered by Anton from a variety of sources - but he knows his stuff (he built me a custom gearbox). From his description, the R1150R (my highlighting below) should have the tall 6th, not the Adv short one...
GAE - early silver R1150GS
GAF - black R1200C (eBay)
GBE - 02 silver R1150RT fluidj
GAL - 02 silver Roadster tall 6th Phil Kavanaugh
GAL - 02, early silver R1150R tall 6th BB, Mihalka
GAN - 02 Adventure
JAE - 03 R1200CL silver on eBay
JAH - black
JAK - 03 black sport GS Neil
JAL - EVO silver Adv.
JAM - 03 black Adventure, RT-P
JAR - Rockster, black (supposedly Sport)
JAS - 04 silver R1150R tall 6th
GAB on eBay, not from an S?
GAE => up to 2003, silver, normal 1st, Serie (= long 6th)
GAF => up to 2003, black R1200C
GAG => up to 2003, black, std
GAJ => up to 2003, silver, normal 1st, short 6th
GAK => up to 2003, black, normal 1st, short 6th
GAN => up to 2003, silver, short 1st and short 6th (only GSA)
GAP => up to 2003, black, short 1st and short 6th (only GSA)
JAE => EVO silver R1200CL
JAH => EVO black standard
JAJ => EVO silver Sport
JAK => EVO black Sport
JAL => EVO silver Enduro
JAM =>EVO black Enduro
JAR => EVO Rockster Sport
JAS => EVO silver standard