Right of way: protected left turner vs Right turner?

Almost had a collision earlier in a protected left turn for me (green arrow). The street I was turning to has two lanes. I was turning left into the right lane but I noticed that a right turner was turning at the exact same time, and she wasn't stopping, so I braked, moved left a little bit, and stopped until I saw that she also stopped.

Who would have been considered at-fault in a collision? For what it's worth, I looked at the other driver, and it seems like she was only looking at traffic to her left, but not in front of her, otherwise she would have noticed that I was turning left.