Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
We apologize for this unintentional delay since we received the question on the weekend and we were consulting medical doctors to learn the nature of this medicine.
After consulting the specialist, we conclude that the medicine (morphine) is among the addictive narcotic medicines. Therefore, basically it is not permitted to use such medicine except in the limits of dire necessity that is determined by a trustworthy doctor.
If the case of this patient is as mentioned then you may accept this job and to inject her with the medicine; otherwise, you should not perform the job.
Allah knows best.