My search is for any details about Werner Achenbach who presumably
married Anna Mary Dye Rice some time during 1937 to 1939 in
Bad-Godesberg. He was in the German Army  and  she returned to her
home in Bedford, Indiana, shortly before the war started. He did not.

Dear philo4,

I am very sorry, but I have to let you know that Werner Achenbach most
likely died in the war. I searched the central database of German
soldiers who died in the World Wars, and I found this entry:

Nachname [Surname]: Achenbach
Vorname [Forename]: Werner
Dienstgrad [Rank]: Obergefreiter [Lance Corporal]
Geburtsdatum [Date of Birth]: 29 October 1916
Geburtsort [Place of Birth]: Rengsdorf
Todesdatum [Date of Death]: 11 July 1943
Todesort [Place of Death]: H.V.Pl.Feld.Laz.m.2/592 [=
Hauptverbandplatz, Feldlazarett m.2/592 - Main Casualty Station, Field
Hospital m.2/592]

I have no doubt that this is the Werner Achenbach you are looking for,
for the following reasons:

- The name is very rare. Among the millions of German soldiers that
died in WWII, there were only three Werner Achenbachs, one of which
was too young to be the husband of Anna Mary Dye Rice, and the other
one came from a region hundreds of miles away from Bad Godesberg.

- Rengsdorf, a small town near the Rhine, is very close to Bad
Godesberg - in fact, the distance is only slightly more than 20
kilometers (12.5 miles).

This leads me to the conclusion that this Werner Achenbach is most
likely the one you have in mind; it's hard to imagine that those facts
are nothing but coincidence. However, the records do not include any
information on the deceased soldiers' families, so it was not possible
for me to check the name of this Werner Achenbach's wife.

Werner Achenbach is buried in a common grave on the Military Cemetery
of Kharkov (Ukraine). The location of his gravesite there is  Block
10, Row 35, Grave No. 4123.
For more information, please contact the German War Grave Care organization:

Volksbund Deutsche Kriegsgräberfürsorge
Bundesgeschäftsstelle
Werner-Hilpert-Strasse 2
34112 Kassel
GERMANY
--
Phone: +49(0)561-7009-114 (or) +49(0)180-57009-99
Fax: +49(0)561-7009-270
E-Mail: info@volksbund.de
Website: http://www.volksbund.de/


However, in case you really want certainty about Werner Achenbach's
fate, you should contact the German Federal Archives. They keep all
remaining personnel records for the German armed forces of WWII. Those
records often also include personal information on the soldiers:

Bundesarchiv
Zentralnachweisstelle
Abteigarten 6
52076 Aachen
GERMANY
--
Phone: +49(0)2408-147-0
Fax: +49(0)2408-147-37
E-Mail: zns@barch.bund.de
Website: http://www.bundesarchiv.de/aufgaben_organisation/abteilungen/zns/


I hope that this will prove helpful!
Best regards,
Scriptor

Genealogies of several Achenbach families were published in "Band 163,
3. Siegerland Geschlechterbuch":

http://www.starkeverlag.de/shopfactory/enter.html?target=GesamtkatalogBuchprogrammDeutsches_GeschlechterbuchSiegerlvdnder_Geschlechterbubcher.html

I'll try to find out if Werner Achenbach is mentioned in this book.

Just to let you know that next week I can look up if Werner Achenbach
is mentioned in the printed genealogies.

The book mentioned in my first comment includes the genealogies of six
Achenbach families (331 pages). Very few of the Achenbachs in this
book are called Werner Achenbach (none of these, apparently, being the
one your are looking for).
A Familienverband Achenbach (i.e. Society of the Achenbach families)
existed in 1973. A webpage of the Familienverband doesn't seem to be
available. Well, at least, it is not listed here:
http://biggislist.genealogy.net/cgi-bin//browse/privat/a