What are the rules for using Banette GX's "Shady Move" Ability?
You can move 1 damage counter from any Pokemon in play to another Pokemon in play; it can be different player's Pokemon or it can be the same player's Pokemon (either you or your opponent).
Source: Celestial Storm FAQ (2018-07-20), TPCi Rules Team (2018-08-02)

Relevant cards

Note: All applicable cards may not be listed below.
SM2_13