So I have a few things to add to this install. If you have it, remove your NAV module. It is very easy and you'll gain a lot more access. There is another clip that the blue cable attaches to that you cannot reach unless you remove the NAV or your radio, I think.
To remove the cable at the white clip point, I simply pressed up on the large white cylinder just in front of the clip and popped it free. See Pic 17 above. Study the clip on your new module for a few seconds and you'll get it.
To install the new cable, it helps to "roll" it into place. If you study the attachment point, you'll see that it is designed to accept the roundness of the cable. See Pic 18. So start with putting the cable into this spot and then "roll" the whole thing to snap the tab back into place. Push on the tab "handle" to do this and it snaps in relatively easily.
Finally, make DAMN sure the vent snaps back into the vent tubes. I snapped mine home without checking this and had to pull the damn thing back out. This is where having access from BELOW the vent/tubes (i.e. why I suggest removing radio/NAV) can help a lot.
2001 530i/5 (E39), Topaz Blue/Stone Green/Black (sold) *very rare interior/exterior color combo*
2005 545i/SMG (E60), ED Order, Titanium Grey/Grey (lease over)
2014 335i/8-spd, Mineral Grey/Black (lease take over)