The pasting occurs when a menuitem is clicked in the floating menu.
I just load text from the SQLite database into a string variable and to paste it at the cursor position I use
AWTRobot.RobotPaste(cm_data)
Perhaps it cannot be used this way, but it works on PC. On Mac it pastes the character "v".
That's why I want to try another way, because I really want my project to work on Mac just the same.