Performing Umre on behalf of a deceased person is permissible according to the consensus of scholars. The reward of the Umre reaches the deceased by Allah's permission. This ruling is derived by analogy (qiyas) from the explicit permission for proxy Hac for the deceased, and from the general hadith that permits good deeds performed on behalf of the dead, such as charity and dua.
Sheikh Ibn Baz stated that performing Umre 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 Umre should have already completed their own farz Umre (for those who consider Umre farz). They should make the niyyah (intention) at the miqat on behalf of the deceased: 'Labbayk Allahumma bi-Umre on behalf of [name].'
Sheikh Al-Albani confirmed the permissibility based on the hadith where Hz. Peygamber permitted proxy Hac for the deceased, and Umre follows the same ruling. He also noted that the person performing the proxy Umre earns their own reward for the good deed, while the full reward of the Umre goes to the deceased. There is no limit to how many proxy Umres can be performed for the same deceased person.