Co. H. Enlisted in Athens, Ga. 1862 and killed 9 june 1863 at brandystation.
see link at bottom where I found the info.
I also saw online the monument at Fairview Cemetery and a H.B.Carter is listed under the Virginia names but not Ga. Do you think they got it backwards and
wrote it as H.B. and not B.H.?

http://www.rootsweb.ancestry.com/~gacogs/search/military/companyHprivatom.html