It has been awhile since I replaced the battery in my B2910, same tractor as the B7800 basically.
It is not that hard to access the battery, but not simple to make a quick measurement either. I remember just buying the largest battery that would fit when I replaced mine. You have to make sure the terminals are orientated correctly.
I would think if you go there and remove the battery and take a measurement to determine the largest that will fit in the space, you should be able to find a replacement locally.
Edit: Of course locally could be quite a distance depending where your dad lives...