The letters below the 13-letter phrase are the other 13 letters of the alphabet, in alphabetic order.
Any given message can be encoded or decoded by finding each given letter among the 26 on the chart, and replacing it with the letter above or below it.
A different 13-letter phrase has been used in forming the key to encyphering a sentence, below. Again, of course that key phrase has no repeating letters.
THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG
is, in this code:
PQS HGCIJ LXMZF NMR KGOTE MDSX PQS BYWA VMU
As was to be expected the replacements are mutual: for example, N codes F and F codes N.
What was the 13-letter phrase used in forming the key to this code?
From the 2013 Mensa 365 Brain Puzzlers for 2013 calendar, puzzle for May 1, by Mark Danna and Fraser Simpson, Workman Publishing, New York, NY.