Yes, the 540's have the 5HP30, which is different than the one for the 530. The tranny on the 530 can't handle to power the 540 puts out. Yes, you could bolt it up to a 540, but I think you'd need a lot of different stuff as well since I think the 5HP30 is bigger than the tranny on the 530. You'd probably need the driveline from the 530, the flex disc, etc.
Certainly don't waste you time trying to fit a 530 auto tranny to a 540 as it's only a matter of time before the 540 destroys a 530 tranny.
Cosmos Black/Black 1995 540iA M-Sport
BMW Individual Exclusive Edition, 1 of 65 total, 9/25/95 Build