I'm actually working with the Mann-Whitney-U-Test and in the test statistic I can't see the Z-Score and the exactly significance. Is there any option to see those figures?

I suspect that you are using Analyze > Nonparametric Tests > Independent Samples. By default prior to version 27, the output is in the form of a Model Viewer, which initially shows just summary information. Double click that object, and you will be able to see all the details.

If you prefer the traditional style of output, go to Edit > Options > Output and select Pivot tables and charts. Then output will be produced in that form instead of as a Model Viewer.

No, unfortunately that didn't worked. I do have those results here:

Mann-Whitney-U-Test:...

Wilcoxon-W:...

U:...

Asymp.Sig.:..

and that's it.

But in Youtube video's I see results like:

Mann-Whitney-U:...

Wilcoxon-W:...

Z:...

Asymptotische Signifikanz:...

Exakte Signifikanz:...

So "Z" and exactly significance are missing.....

You haven't said which procedure you are using, but the option for exact significance level is available via Analyze > Nonparametric Tests > Legacy Dialogs > Two Independent Samples. However, it requires the Exact Test option. To see whether you are licensed for this option, run SHOW LIC in a syntax window. Also, if you have this option, you will see a button labelled Exact in the dialog.