A similar entry appears in the Wheel of Time Companion confirming the information available in the main story arc.
Author: Atarah al'Norahn
Apparently his wife had "the falling sickness", and so he never questions Ronde Macura as to who she sends messages to or why; possibly she Healed his wife.
When Ronde Macura wakes up after Elayne and Nynaeve have escaped, she goes to Avi Shendar's place and sends off two pigeons, one to the northeast (toward Tar Valon), and a copy of the note to the west. Avi pays no attention to her, but after she leaves, he picks up a sheet of paper that was beneath the one she was writing on, so he can see what she wrote. As he always does, he makes a copy of it and sends it off in a third direction; to whom is not known.
(Reference: The Fires of Heaven, Chapter 10).
"Hoeing in his garden patch as usual, Avi paid no attention to what Ronde did. And as usual, as soon as she was gone, he washed his hands and went inside. She had placed a larger sheet of parchment underneath the strips to cushion the nib of the pen. When he held it up to the afternoon light, he could make out what she had written. Soon a third pigeon was on its way, heading in still another direction." (The Fires of Heaven, Chapter 10).