Just checked the Sargent website and it list the same seat for R1200gs\1250gs 2013 on .
So presume that means they will fit.
Check the website :--
https://www.sargentcycle.co.uk/acatalog/r1200gs-lc-2013-front-and-rear-seats.html
Also --what are you trying to achieve with the Sargent seat ? --more comfort??
Might be worth trying one of the cheap mesh covers from Ebay , I just fitted one to my 1250 and I'm pleased with the extra comfort\feel so far. Ignore the sales pitch about being cooler in hot weather (it may be but not at this time of year) , it's mainly the extra cushioning\weight spread it gives. If it's no good you'll be £3.65 worse off --if the Sargent is no good you'll be £200 to £400 worse off

.
I feel like a salesman for them

, put another link on the "coolcovers" post earlier this week but I have no interest in them other than having bought one and being impressed with it for the price.