I know they work up till 08. 09-12 they went to a big piston front froks and the tubes where larger, however 13 was the first year of the 636 so I’m not 100% but I would say no
I believe in 2013 the 636 had a Big Piston Separate Function Showa while the 06 had a conventional 41mm Showa
You'll have to use the triple clamp from the '06, as well as the front wheel and most likely the brakes. You'll lose the front speed sensor if you got that route too, so the speed won't be displayed on the meter, you'll have a trouble code showing and TC won't work.