Performing العمرة on behalf of a deceased person is جائز عند the consensus of scholars. The reward of the العمرة reaches the deceased by Allah's permission. This ruling is derived by analogy (qiyas) from the explicit permission for proxy الحج for the deceased, and from the general hadith that permits good deeds performed on behalf of the dead, such as charity and الدعاء.
الشيخ ابن باز stated that performing العمرة on behalf of a deceased parent, relative, or any Muslim is a righteous act and a form of birr (kindness) that benefits the deceased. The person performing the proxy العمرة should have already completed their own واجب العمرة (for those who consider العمرة واجب). They should make the niyyah (intention) at the الميقات on behalf of the deceased: 'Labbayk Allahumma bi-العمرة on behalf of [name].'
Sheikh الألباني confirmed the permissibility based on the hadith where النبي permitted proxy الحج for the deceased, and العمرة follows the same ruling. He also noted that the person performing the proxy العمرة earns their own reward for the good deed, while the full reward of the العمرة goes to the deceased. There is no limit to how many proxy العمرةs can be performed for the same deceased person.