Not 100% sure. Mine is a Sept 2003 N62 4.4i build and I think the 6HP19/21 was only used on the 7 series at that point. Wayne said earlier in the thread that he had the same issue on his E53. Fcpeuro.com said it was the correct part for my vehicle.

I found this by searching for 6HP19/21 n62:

The 6HP19/21 is a 6-speed automatic transmission for BMWs. It was developed from the original 6HP26, but was downgraded for less demanding applications. The 6HP19 is rated at 400 newton-metres (295 lbf⋅ft) of torque.
The 6HP19/21 was installed in many cars and BMWs with different engines, including:
2006-2013 BMW 3 series (E9x)
2007-2012 BMW 1 series (E82)
2002-2008 BMW 7 series (E65, E66)
2009-2013 BMW 7 series (F01, F02)

The 6HP19/21 fits the following BMWs:
BMW E60/E63/E64 545/645 N62
BMW E53 X5 N62