I have always thought that William F. Grimsley originally enlisted into Company F, 16th Tennessee Infantry, on the date that you have listed, not Company K.
You have pointed out an interesting fact concerning William L. Grimsley, concerning the correspondence between th Adjutant General War Department and the Oklahoma Board of Pension Commissioners dated August 11, 1915.
If possible, could you send your information via my email address instead of this message board?
Thank You,
Tim Young
145 Old Stover Rd.
Monroe, TN 38573
(931)403-0990