Aloha, Good Sir!
Others will be able to verify, but for a start check vol. I of the history the Braunschweig Infantry Regt'l history by Kortzfleisch, which gives the following:

p. 136: organized into twelve companies before departing for Portugal (3rd Company was Scharfschützen)

Initially assigned to the 4th Division (Packenham's Bde).

pp. 158–160: on 12 November, the Braunschweigers were redistributed:
- 3rd Company remained with Packenham's Bde of 4th Division
- 2nd and 10th Companies were assigned to the 1st and 2nd Bdes of 5th Division respectively
- the remainder went to the 2nd Bde of the Light Division

Again, hope others can validate, but Kortzfleisch is quite detailed and thorough.
Hope that helps.