Praise be to Allah.
It is not permissible for the boss or manager of the department, or whoever is acting in their stead, to agree to anything that he thinks is not right. He has to check on the matter. If there is any need for this request due to an urgent need and if giving permission will not affect the work, then it is OK. But if he knows that an excuse is false or he thinks it is most likely to be false, then he should not give permission and should not agree to it, because that is a betrayal of trust and a lack of sincerity towards the one who put him in this position of trust and towards the Muslims. Allaah says (interpretation of the meaning):
“Verily, Allaah commands that you should render back the trusts to those, to whom they are due” [al-Nisaa’ 4:85]
And Allaah says, describing the believers:
“Those who are faithfully true to their Amanaat (all the duties which Allaah has ordained, honesty, moral responsibility and trusts) and to their covenants” [al-Mu’minoon 23:8]
And He says (interpretation of the meaning):
“O you who believe! Betray not Allaah and His Messenger, nor betray knowingly your Amaanaat (things entrusted to you, and all the duties which Allaah has ordained for you)” [al-Anfaal 8:27]