If it's a 4.8, then you should use the numbers for your specific vehicle. The 4.4 has different numbers. these numbers I believe have to do how the transmission will perform - the 4.8 has a different engine, and probably will have different shift rpm values, etc. And you should use both numbers:
EGS programmed number 7 564 921,
EGS basic number 7 557 063
Not sure how the TIS should come back to you with the 4.4 numbers? Progman handles the coding & re-flashing. The TIS is the skinny version of BMW's DIY. And the updated technical bulletin service was released years after the TIS.

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Stable: e92is, e46 M54B25, e83 N52, e53 N62 - sold, e39 M54B30 R.I.P.