Ok, this is a completely do-able task, but step one is to break it down into its constituent components and then figure out how those need to go together. Perhaps start by making yourself a flow chart so you can determine what components you'll need, then we can tackle those one at a time.
For example, one of the components you might need is a function to determine whether a given textFrame (the text inside your circle) matches the name of a given artboard.
function frameTextMatchesArtboard(text,artboardName)
{
//return a boolean value representing whether the given text matches the given artboard name
return text === artboardName;
}
then elsewhere in the script you would use that function to determine whether to duplicate your object into the other document, like so:
//using somewhat silly variable names so it's very clear what i'm talking about
var arrayOfCircleObjects = [];
//do something to populate the above array, a simple loop with the array.push() method would work great.
var arrayOfDestinationArtboards = [];
//again, populate this array with a loop in the same manner
//now depending upon the number of objects and artboards you're working with, you'll nest one loop inside another to compare the text to the artboard names. the number of objects determines which loop will be nested inside the other.
var currentCircleObject, currentCircleText;
var currentArtboard;
for(var x=0, len = arrayOfCircleObjects.length; x < len; x++)
{
currentCircleObject = arrayOfCircleObjects;
//here you'll need to do something to get the contents of the textFrame contained within this object
currentCircleText = getCircleText(currentCircleObject);
//now loop the artboards from the other document
for(var y=0, yLen = arrayOfDestinationArtboards.length; y < len; y++)
{
currentArtboard = arrayOfDestinationArtboards;
if(frameTextMatchesArtboard(currentCircleText, currentArtboard.name)
{
//duplicate the circle object to the other document
}
}
}
I know this isn't the complete answer you were looking for, but i believe there's tremendous value in being able to work through the problems on your own.
If you have any specific questions on how this stuff works or how to do something, i'm here. Hopefully the above examples help put you on the right track.