@Inna22 If the guest is leaving early because of a change of her circumstances, not because she is unhappy with the listing, I don't know why you would give her a partial refund. You have lost that night's booking, not half of it. Maybe explain that to her and that you are not allowed to take one night bookings.
I guess it also depends though on the length of stay and if the charge for half a night is such a big deal, i.e. is it worth making a fuss about. I refunded guests who left a day earlier because they got a cheaper flight, but that was a 3.5 month stay, so one night was hardly significant.
If you want to refund her for half a night, just calculate what that would be and send her a payment via the resolution centre. Explain that you can't refund the Airbnb fee portion as that doesn't come to you.
Interesting though that the Airbnb insurance for guests only covers full cancellations and not partial ones.