My question is simple:

When you have a multiple regression equation which is:

Y = a0 + a1.X1 + a2.X2 + a12.X1X2

is it correct to remove a2.X2 if a2 is not significant and a12 is significant.
I have seen conflicting answers, some saying (without a lot of justification) that It shouldn't be removed and others saying that it can be removed since you can write:

Y = a0 + a1.X1 + a2.X2 + a12.X3
Where X3=X1X2

Also, I usually makes stats using JMP and the software allows both possibilities...

IMO you should not remove it.Think of a location transformation of X1->X1+c then X3->X2(c+X1) and the model gets a0+a1X1+ca3X2+a4X1X2, so you get stuck with X2 again while not doing anything with it,you simply shifted X1 (the same holds if you simply change the scale of X1!)