Vector orientation mismatch between FSL & MRtrix

So finally I could solve the problem! I splitted my 4d volumes into 3x 3d volumes and multiplicated the first volume which representing the x-coordinate with minus one. After that I re-concatenate the volumes to a 4d volume. Commands like fslswapdim or changing just the L/R convention didn’t achieve the desired results.
Maybe another important thing to call attention to was that the gradient values in the mif files are not the same as in the bvec files of the same diffusion data. The first row (x-coordinate) is multiplicated with minus 1! So I guess converting the nii data to a mif data which includes the gradient vectors an b-values is also changing the orientation?

Anyway thank you for your help!
Cheers
Max