Biggest thing is make sure the are the same chemistry and voltage batteries first, just to get that out of the way. I'd also want to make sure the Brawler battery had a built in protection board before wiring it up, and that it's not just a straight battery pack, though anymore they pretty much all do.
The T connection is most likely for a Thermistor that is inside the Pro battery pack so the charge controller can keep watch on it, but it could be some disgustingly complicated one wire data connection also. Swapping the Brawler pack to the Pro using just the + and - may or may not work, depending on what the Pro controller is expecting to see on that T line. You could measure the Pro battery T to - and see what Ohms value it gives you and then warm the pack up just a touch with a hair dryer and make sure that value changes, then you'll know it's just a Thermistor in there. Then take that room temperature value and eihter install a new Thermistor or just a plain jane fixed Resistor at that value, but caveat, then it will not be able to keep watch on the battery temperature if you do the fixed Resistor. You could carefully open the Pro battery up and use that one, though it may be built into the protection board that's in there.
Tossing the Pro battery into the Brawler would be easier, just ignore the T connection on the battery, but then it will also probably get you about an hour of game time before needing to be recharged.
