This document to inject connect messages in Connect support or peer to peer connect conversation via script

Scripting assistance

If you can get the chat conversation live_group_profile id(You can query the current live_group_profile table with chat_queue_entry reference) then you can try posting using the LiveFeedMessage().postMessage() API. 

var convId = "SYS_ID"; //live_group_profile sys_id of chat conversation
var lm = new global.LiveFeedMessage();
var data = {
"message": "MESSAGE NEEDS TO BE POSTED",
"group_id": convId,
"from_profile":"SYS_ID" //live_profile sys_id of a user. The message will be posted on that user's behalf
};
lm.postMessage(data);

Please refer OOB Script Include - LiveFeedMessage - for more details about the data object. Invalid sys_id for "from_profile" will insert the message as posted by "system".