The best way to identify manufacturer of drive is to look at position of emergency eject hole and position of drive led.
BenQ at center of front, Lite-On at the left side of front.
BenQ at right side, Lite-On at left of center.
From pic on HP page I assume this drive is BenQ 1625 in external enclosure. Compare with Lite-On (Philips) external drive. here
BTW, Nero InfoTool can also give you useful information about any optical drive.