Working and earning livelihood through a halal (lawful) source of income is a basic requirement in Islam. It is also a source of dignity and self-esteem. The Prophet (peace and blessings be upon him) taught his Companions that the whole of a human being’s dignity is tied up with his work, and that real disgrace and humiliation consist of depending on other people’s help. The Prophet is reported to have said, “It is better that a person should take a rope and bring a bundle of wood on his back to sell so that Allah may preserve his honor, than that he should beg from people, (regardless of) whether they give to him or refuse him” (Al-Bukhari and Muslim).
Thus, Muslims are Islamically encouraged to work as long as they sticks to the Islamic manners in their work and avoids doing anything that is haram in Islam. As for working in the post office, there is nothing wrong with it as long as Muslims avoids signing, writing, filling in applications, or being a witness to a riba contract.
Dr. Monzer Kahf, a scholar in Islamic economics and a financial expert, states the following: Working in a bank, post office, or other organizations that deal with riba to a lesser or larger degree is permissible as long as one avoids signing, writing, filling in applications, or being a witness to a riba contract.
There are many jobs in banks and other institutions that do not deal with such functions. A post office has even much lesser contact with interest contracts. Yes, it is permissible to work in the post office with this condition.