Thank you for the great support!

After engine start and after the 2min for the glow plugs, I had the voltage at 13,6V the engine rpm is in this case between 1600 and 1800.
The battery isn't full, because the voltage at the battery is 12,0-12,2V when I turn off the engine and wait a few minutes.
Where do I check the FICM voltage?
In Germany we had to change the trailer wires to a 13pole connector with a special cable. The core size is 2,5mm˛ (sorry, I don't know the american spec for this size). It could be a little bit bigger core size, but it works.
Now I'm not sure, what to do. But I think the 185A alt from dc power you recommended should be the solution!

Because you had to log in to the Dodge-Forum.eu to show, the pics, of my truck, I do the pics in this post!