Is it permissible for a son and his mother to perform 'Umrah on behalf of the deceased father at the same time, and as the same 'Umrah?

It is permissible for two people to perform Umrah on behalf of one person at the same time, with each of them performing a separate Umrah for that person. If a person deputizes two individuals to perform Hajj or Umrah on their behalf, then the one who enters into ihram first will have their Umrah or Hajj counted as the obligatory one, and the other will be supererogatory. Accordingly, it is permissible for both of you to perform Umrah on behalf of your deceased at the same time, provided that each of you performs a separate Umrah intending it for the deceased.