I have parented the mesh now a dozen times, but now all the vertexgroups are right the mesh does not respond to the rig, I am afraid that I have to parent the mesh from scratch obj, but I hope for another solution, sorry if this does not work. (of course I have done weight painting but this did not help)
Just from your screenshot I can see that you have not made the parented “virtual” armature modifier “real” in the modifier stack … Go ahead and “make real” the armature modifier and turn on only the vertex group option on (and not the envelope option) and see if that helps .
You might have both vertex groups and envelopes turned on for the armature and this might be the cause of your problem … if you have the proper vertex groups assigned then just turn off the envelope option as this can interfere with proper mesh deformation … Just go to the armature panel in F9 (Editing) context see if both vertex groups and envelopes are turned on (they are both on by default) … if they are turn off the envelopes option there as well as in the modifier stack …
If none of this helps then just post the blend …
I think I will find it out while I am setting up the vertex groups, otherwise I think I will post my blend file again.