Thanks for the manufactures name-
PN 16116755043 is the part number for the "kit"

From what I am finding, there are 2 Pierburg pump part numbers listed for E53
7.50138.00.0 and 7.22013.57.0
and from my search only UK suppliers for pierburg pumps without the sending unit.

Bosch also makes a pump, part #0986580130, which I think also includes the screen.

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2004, X5, 3.0, 202k+