z_a: You'll need to identify your K240 version - the older models (Sextett, Monitor (M), DF) all have hardwired cables, while the newer Studio (S) version features a detachable cable. The latter comes in two variants, though: The initial version had a 2.5 mm micro plug (that's the version you can see in mrarroyo's picture), which was then changed to Mini-XLR with the introduction of the K271S - that version is internally named K240 Studio II, but not marketed as such. In any case, the next best step would be to download AKG's service documentation for the K240 from their site (go: Library -> Download -> Service Documentation - doesn't work for me at the moment, though: I get an error message...): K240_m_stu4055d215ac91a.pdf is the latest version I have. In there you will find the appropriate replacement part numbers for all K240 models, so you can order these via dealer or directly from AKG.
Greetings from Munich!
Manfred / lini