2005 Triumph Daytona 955i - Rr Connector Conundrum!

Hello first post here so to introduce myself, i'm a rider of 5 years, still with my first 'big' bike; my 2005 Triumph Daytona 955i. It's been a dream for the 3 years that i've had it, but I have had intermittent electrical issues. These peaked last month and after replacing the battery (a veteran of several Winters) and I decided to change the RR.

The replacement I bought has a 3 pin connector in a triangle arrangement for AC power and a 4 pin connector in a square arrangement for the battery (2 red wires, 2 black wires).

The old one that I removed has a 3 pin connector in a flat arrangement for the AC power and a green and a red wire with ring terminals for the battery.

The question is how can I fit the new one in place of the old one?

3 PIN AC
Can I change the connector over? And am I right in thinking it doesn't matter which order around the wires connect in?

BATTERY
Can I just de-pin the connector on the new RR and fit ring terminals to the two red and two black wires, and connect to the battery terminals?

Hopefully it's not too much of a head scratcher. Any advice is greatly appreciated!

Image 1: New RR

Image 2: Old RR showing both AC power & battery connectors

Image 3: Old RR showing AC power connector pin arrangement