die Berechtigung
authorization
The official right or permission to do, have, or use something.
Haben Sie eine Berechtigung, diesen gesicherten Bereich zu betreten?
Do you have authorization to enter this secured area?

authorization / justification
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authorization
The official right or permission to do, have, or use something.
Haben Sie eine Berechtigung, diesen gesicherten Bereich zu betreten?
Do you have authorization to enter this secured area?

'Die Berechtigung' (authorization/justification) is derived from the verb 'berechtigen' (to authorize), which in turn comes from the noun 'das Recht' (the right, law). So it is always about a granted right.
Ohne eine gültige Berechtigung ist der Zutritt verboten.
Without valid authorization, entry is prohibited.
The meaning 'Erlaubnis' (permission) usually refers to a concrete action. The meaning 'Rechtfertigung' (justification) is more abstract and refers to the validity or point of something.
Er braucht eine Berechtigung, um die Software zu nutzen.
He needs authorization to use the software.
In the meaning 'Erlaubnis' (permission), an infinitive construction with 'zu' is often added to describe what someone is allowed to do: 'die Berechtigung haben/bekommen, etwas zu tun' (to have/get authorization to do something).
Mit dieser Karte haben Sie die Berechtigung, alle Türen zu öffnen.
With this card, you have authorization to open all doors.
In the meaning 'Rechtfertigung' (justification), the fixed expression 'seine Berechtigung haben' is very common. It means that something is justified or meaningful.
Jede Meinung hat in einer offenen Diskussion ihre Berechtigung.
Every opinion has its justification in an open discussion.
right / law
'das Recht' and 'die Berechtigung' are close in meaning when someone is allowed to do, use, or demand something. 'das Recht' is the more general word and fits legal or moral claims. 'die Berechtigung' often sounds more official and more concrete, for example for access, an ID, or a task. In addition, 'Berechtigung' can also mean a good reason why something is right or meaningful. The words can be confused because both express a claim or entitlement. In everyday life and basic rights, 'Recht' is more natural; for official access rights or responsibilities, 'Berechtigung' often fits better.

Die Mitarbeiterin prüft heute die Berechtigung für den Zugang zum System.
The employee is checking the authorization for access to the system today.
Meine Mutter sagt, dass jeder das Recht auf eine eigene Meinung hat.
My mother says that everyone has the right to their own opinion.