Hi Marcus,
Based on my experience, it probably won't fit easily. I bought a Remus Evolution can (also a good price) which was stated to fit a K1300S in the add, but as actually for the K1200. What I found is that the K1300S downpipe is longer, because of the flap valve , which then pushed the can further back on the bike and the mounting holes to the passenger foot peg no longer lined up. I swapped the mounting from the standard fixed bracket to a simple strap, which I could position as needed, but it was not ideal. I would be inclined to look out for the right can.
Jason