What is the ruling regarding a police officer who does not pray during working hours and performs the prayers upon returning home, and is he permitted to do so?

Your brother is not permitted to intentionally delay the prayer beyond its appointed time, for this is one of the gravest transgressions and major sins. He must perform each prayer within its designated time according to Islamic law. If he has an excuse that allows for combining two prayers, then he may do so. However, an employment contract is not among the excuses that permit combining prayers, unless he is hired to guard property that he fears might be damaged, or if he fears harm to his livelihood by not combining them. In such cases, some scholars allow him to combine prayers. But if he is unable to perform the prayer on time, even by combining them, then he must leave this job and seek another that does not conflict with performing prayers at their appointed times.