Is it permissible to perform Umrah on behalf of a deceased mother whom her son had promised to sponsor her trip for Umrah?

It is permissible to perform 'Umrah on behalf of one's deceased mother if the person performing 'Umrah has already performed it for himself. The evidence for this is what Abu Dawud and Ibn Majah narrated from Ibn Abbas, may Allah be pleased with both of them, that the Prophet, peace and blessings be upon him, heard a man saying, "Labbayka عن Shabramah." He asked, "Who is Shabramah?" The man replied, "A brother of mine, or a relative of mine." He asked, "Have you performed Hajj for yourself?" The man said, "No." He said, "Perform Hajj for yourself first, then for Shabramah." 'Umrah and Hajj are the same in this regard.