I found this information courtesy of the Civil War Data website (it is a pay website that I belong to). It seems to match the information (except for the wife's name) you have provided above. Keep in mind, it is not uncommon for him to have perhaps been married once or twice, perhaps a marriage no one knew about. The person listed below as his widow could have been his first wife who never knew he remarried, or could have been trying to get the pension since she was married to him at the time he was in the service, etc. I found a few instances of this, and only by perusing the file will you be able to sort it out in most cases. Gives you the pension file number and so forth, should you decide you want to order it. Hope this helps some, and good luck! I have several relatives that served in the 39th as well, but different companies from your ancestor.
Residence was not listed;
Enlisted on 11/1/1862 at Peach Orchard, KY as a Private.
On 2/16/1863 he mustered into "A" Co. KY 39th Infantry
He was Mustered Out on 9/15/1865 at Louisville, KY
Federal Pension Information:
He applied for a pension on 9/11/1879
application # 308,803
His Widow (Mary E Adams) applied for a pension on 6/22/1906 from the state of OK
application # 851,122
Sources used by Historical Data Systems, Inc.:
- Report of the Adjutant General of the State of Kentucky
(c) Historical Data Systems, Inc. @ www.civilwardata.com