Submitting a note on the falsehood of a conjecture to the journal the conjecture originally appeared in I wrote a short note, showing that someone's recent conjecture is false. Is it a good idea to submit the manuscript to the same journal the conjecture originally appeared in? Will it expedite the reviewing process?  

Update: After reading the comments in here and talking to my advisor, I ended up submitting the manuscript(including the counterexample and a little improvement of the original result) to the same journal as the original was appeared in. Paper got accepted in less than 40 days. I highly believe in my case, choosing the same journal shortened the reviewing process significantly.
Submitting your manuscript to the journal the original conjecture was published in is probably a good idea. After all, if the journal published the original conjecture, then the conjecture is obviously in the journal's scope... and so should be a counterexample.

In addition, your submission may well be handled by the same associate editor, who may be able to call on the same reviewers as for the original conjecture. (Of course, it would be a good idea to get at least some new eyes to look at matters, to avoid academic inbreeding.) This could accelerate the review process somewhat.

Beyond that, you likely won't get any preferential treatment beyond what the shortness of your manuscript and the immediate relevancy of your counterexample warrant.