I saw an Opel Blitz with Einheitsfahrerhaus in a green-red paintscheme at a vintage truck meeting last year.

Construction truck with a cement mixer, bricks and pavers, shovels, etc....?

One should understand that immediate after the ending of WW2 the German economy was down on its knees completely (as it was the case in many European countries).
Enterprises had to restart and new ones used the momentum of the enormous possibilties peace brought. The Marshall support plan was a big help. So, all together, plenty ideas, enormous challenges, but hardly any proper tools to start with. Therefore the surplus of the various armies, both Axis and Allied, were sourced for usable equipment. Trucks, engineeringing machines like bulldozers etc. were released from their army duties and went into civil hands. Not seldomly in the same status as their military life. All following the motto "if it works, it works!". However: to make yourself known as an entrepreneur you have to differentiate from the rest. So repainting started (Miniart's MB 1500S as a good example).
Being from the mid 50-ties I can remember mixes of US halftracks with cranes or draglines on it and GMC tippers, painted in the colours of well known construction cies. Ex-army trucks in civil outfit drove around until the end of the 60ies.