Window leaking from moulding
Were it my home I'd be removing the gray exterior casing to find out just exactly how the window is flashed. You can't fix bad flashing from inside. You can stop the interior leak, but the water will go on its merry way rotting your wall out. 

I'd also want to know what kind of drain plane is behind the stucco, if any. That will determine whether you should flash behind or in front of the stucco. 

Can't say much more with what I know from your post. Update if you decide to get into it.