Have a quick look at this service file for (I think it’s 20408 Rosbrook) it might be helpful link to two pages FindMyPast, you can check the whole file if you think it’s useful Click Click
Not 100% certain but ran this through AI and The link is for 20408 Rosbrook, but if you scroll through to pages 0450–0454 in that same Findmypast file, it actually includes the B.103 Casualty Form for 20406 (William Ernest Thomas).
His B.103 gives the exact pipeline: landed at 33rd IBD in Sept 1917, attached to No. 3 Entrenching Bn in Feb 1918, and then posted to the 1/5th West Yorks in May 1918. You need to check and if this is not useful blame AI if it is useful, I’ll take the credit
Mike