Thanks for writing in! I'm sorry to say that you will not be able to replace the string alone. Since it is hanging in the window in the way that it is, it is likely that you'll need to replace the entire channel balance. With that said, I'll need to see a photo of the balance removed from the window to identify the correct replacement.
I am specifically looking to see a photo of the any attachments on the top and bottom of the balance. I'll also need to know the length of the metal channel and the stamp/marking from the channel. If possible, it would really help to see an undamaged balance.
In the meantime, your pivot shoe looks like it could be our 15-129. To confirm that this is the right replacement, carefully look over the dimensions and compare them to your existing shoe.
Jasmine isn't in today but I'd be happy to assist from here. Our Series 770 comes to mind. This comes attached with the 15-043 terminal clip so you'll want to make sure yours looks the same. As for the pivot shoe, you may also want to take a look at the 15-135. We also sell the 19-029 and 19-030 S-clips which are sold separately.