What is the ruling on working as an officer in the army, knowing that admission was gained through nepotism despite the presence of others with higher qualifications, and the parents are aware of and pleased with this?

It is not permissible to use intercession (wasta) to obtain jobs or public opportunities if it leads to prioritizing someone over another who is more deserving, because this involves injustice and deprives the competent. However, if using wasta does not result in the loss of anyone's right, then it is permissible and even desirable. One must repent from forbidden wasta, but there is no obligation to leave the job obtained through it as long as one performs it as required.