I am using the same FF you have (very satisfied with it too) I use a smaller 5 amp battery and get around one and a half day's (probably around 16 hours) use before the battery drops to 8 volts and the FF won't work anymore. if a picture is worth a thousand words...........
go to this post and look at how I have my FF mounted:http://www.hobiecat.com/forums/viewtopic.php?f=78&t=33618
from the picture in the link to the battery you ordered it looks like the battery is wired to the external female plug, you will probably need to wire the male part of the plug to your positive and negative wires on your FF. If there is not a fuse inside the battery compartment I would put a fuse on the male side of the wiring plug. be sure and keep extra fuses on hand.
Thank you... I chose this FF after reading / seeing your post. I was looking at setting it up the same way you did but I am still playing with shooting the Transducer through the hull. It really comes down to less parts to buy right now because I am ordering a second transducer to move this FF from the PA to my boat.
The question about the battery also came from the dealer who led me to believe I need a wiring harness to connect the battery and I didn't know what he was talking about. Since the post I now know that I misunderstood him. Anyway I knew about the inline fuse if it is not installed in the prewired battery box but would you know what amp fuse is needed for the 788ci? I will look in my manual.