2/22 London Regiment & 1st RIR

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My grandfather was KinA 15 November 1916 as Pte 7116 2/22 London Regiment, formerly 5829 3/24 London Regiment. His medal Roll shows 22 London from 30 Sep 1916 to 28 October 1916, then 1st RIR 29 October to 15 November. There is no mention of the 3/24th.

Records for the 1st RIR mention a draft of mostly Londoners joining at Citadel Camp on the 31 October. The War diary shows 13 OR killed on 15th November-probably one of these my grandfather.

I'd like to trace his tracks from June 6 when he appears to enlist up to the time of his death. Can I assume that he goes from 3/24 to 2/22 London and then is attached to 1st RIR and when was he likely to embark for France?