This is a tough one. Looks like you need a connector for a Dolphin battery, and your kit puts a controller into the battery cradle. I;ve looked myself in the past, and that's covered in this old thread. I was able to find one end.
https://endless-sphere.com/forums/viewtopic.php?f=2&t=93846&p=1376248#p1376248
Those Dolphin packs are getting scarce. I've got two bikes that still use them. There must be a lot of these packs all worn put now. Mine are five years old, but I plan to re-stuff them with cells when they can't hold power. However, maybe someone will sell you the shell and cradle for peanuts.