I can't confirm that Truppsoldat is a soldier in a combat unit, but I think this might be the case. Trupp would be in contrast to an administrative unit, i.e. an army unit that would not be deployed in the front lines. Fernsprechtrupp could be telephone communications section. For Soldat I would use specialist.

Private First Class XYZ was deployed to a telephone communications section in a combat unit ... he was trained as telephone communications specialist

Nachrichtenstaffel, communications section
 Fernsprechtrupp - wire communications group
 Funktrupp - radio communications group
http://www.miniatures.de/html/ger/toe-1939-german-mg-kompani...

Nachrichtenstaffel (transmission) mit Fernsprechtrupp und Funktrupp (one radio and one telephone squad)
http://www.armchairgeneral.com/forums/showthread.php?t=43022

Trupp
(lit. Troop; Section) A small unit, equipped with specialized equipment; it could also be used as the designation for a headquarters echelon unit (Kompanie-Trupp: Company Headquarters; Zug-Trupp: Platoon Headquarters, etc.).

http://niehorster.orbat.com/011_germany/symbols/_symbols_39....

telephone communication section

The typical US Army signal battalion is comprised of a satellite section, a radio section, a telephone section and a networking section. It is normally commanded by a lieutenant colonel, with three to five signal companies. The signal company commander, normally a senior captain, oversees several platoons that contain one or many of the aforementioned signal specialties.
http://www.answers.com/topic/signal-corps

in der britischen Armee