Green’s Dictionary of Slang

convo n.

[SE conversation + -o sfx (3)]

(Aus./N.Z./US black) a conversation.

[UK]K. Lette Foetal Attraction (1994) 214: A mate of a mate overheard a convo at the Groucho club. Said you were in the poo and might want to sell your story.
[NZ] McGill Reed Dict. of N.Z. Sl.
[US]Chicago Trib. 22 Aug. TAB-23/3: The former pair have been dating for eight months; the latter has been avoiding the marriage ‘convo’.
[UK]A. Wheatle Crongton Knights 187: Venetia had a serious crush on a teacher [...] (Bit didn’t love that convo at all).