I know that in order to utilize a B15/P11 transmission in a B14 or B13 series, you have to custom modify the transmission from hydraulic to cable actuated. Which is not that difficult if you know what you are doing with a wrench.
Therefore I am *guessing* that you would have to convert the B14 tranny from cable to hydraulic actuation in order to use it in your B15.
However, I have no idea if my *guess* is correct, nor whether you can change things in that direction.