What is the ruling on working as a post office director if this task is free from the usury-recording process carried out by some employees?

There is no harm in working at the Post Office as long as it does not involve anything forbidden, such as recording usury in savings accounts. This is based on the hadith (definition) narrated by Jabir, may Allah be pleased with him, that the Prophet, peace and blessings be upon him, cursed the devourer of usury, its payer, its scribe, and its two witnesses. It is also based on the words of Allah the Almighty: (And cooperate in righteousness and piety, but do not cooperate in sin and aggression.)