Inasmuch as both were residents of Muscogee County, they could have been traveling home in company.
C A. Klink

Residence Muscogee County GA;
Enlisted on 8/14/1861 as a 2nd Lieutenant.
On 8/14/1861 he was commissioned into "F" Co. GA 17th Infantry
(date and method of discharge not given)
He was listed as:
* POW 5/23/1863 Richland, PA
* Paroled 2/15/1865 Johnson's Island, OH (Estimated day)
* Transferred 2/20/1865 Point Lookout, MD (For exchange)
Promotions:
* Adjutant (As of Co. S)
* 2nd Lieut 5/15/1862 (Estimated day; resigned as Adjutant)
Intra Regimental Company Transfers:
* from company F to Field & Staff
* 5/15/1862 from Field & Staff to company F (Estimated day of transfer)

.....

Lawrence Eugene O'Keefe

Residence Muscogee County GA;
Enlisted on 8/14/1861 as a Jr 2nd Lieut.
On 8/14/1861 he was commissioned into "C" Co. GA 17th Infantry
(date and method of discharge not given)
He was listed as:
* Transferred (date and place not stated) (To Trans-Mississippi Dept.)
* Wounded (date and place not stated)
* POW 5/23/1863 Richland, TN
* Paroled 2/22/1865 Johnson's Island, OH (Estimated day)
* Transferred 2/24/1865 City Point, VA (For exchange; no further record)
Promotions:
* Capt

Sources used by Historical Data Systems, Inc.:
- Roster of Confederate Soldiers of Georgia 1861-1865

.........

There is no record of Klink on his Company F January/February, 1863 muster roll, which could indicate he had been dropped from the rolls previously. This may have been because of transfer to the Trans-Mississippi. Unfortunately, there are no prior Company F muster rolls in the records

Lawrence O'Keefe, Tenders resignation February 23, 1863, his Company C, Muster roll for Jan/Feb, 1863, in camp near Richmond, Va., records him as Absent, Absent without leave