Coordinate Transformation

I need to make a coord transformation from Unity into another system. Unity is left handed my other system is right handed in particular I have to negate the z-coordinate. atm. I have only one problem regarding rotation: I started with read of eulerAngles and transform those to Quarternions but regocnized that I have to many cases....

Has anyone a clue how I can do a coordinate transformation via Quaternions directly or any other solution.

Ok I find it out myself. Normaly you have to nothing, because quaternions are independet of handed coord. systems. In my case I have to manually switch again and you can do this like ,q,q.w,-q.x,-q.y,q.z