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I think I misunderstood your problem. The lilian didn't come off the tip, it just became lodged in the second section, right? Did you take off the butt cap? Ususally the tip section is slightly...

It's a pretty simple process, if it helps, I've posted some pictures to show the process -

http://tenkaraflyfish.webs.com/apps/blog/

(about half way down the page)