Yes, there is no issue with that, provided the person has performed Umrah and Hajj for themselves first. Here is a detailed explanation:

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Rules and Conditions:

1. Performing Umrah and Hajj for Oneself First:
   The person must have completed Umrah and Hajj for themselves before deputizing on behalf of someone else for either. If they have already performed Umrah and Hajj for themselves, it is permissible to perform these acts on behalf of others, whether for payment or without charge.

2. Deputizing for Others:
   After completing their own Umrah and Hajj, a person may perform Umrah or Hajj on behalf of others, whether the other person is deceased or unable to perform these acts due to old age or illness.

3. Tamattu' in the Same Year:

   • If someone performs Umrah on behalf of another during the months of Hajj (Shawwal, Dhul-Qi’dah, Dhul-Hijjah) and then performs Hajj for themselves in the same year, they are considered to be performing Tamattu'.
   • Similarly, if a person performs Umrah for themselves during the months of Hajj and then performs Hajj on behalf of someone else in the same year, they are also considered to be performing Tamattu'.

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Practical Examples:

1. Performing Umrah for Someone Else and Then Hajj for Oneself:
   If a person performs Umrah on behalf of someone else during the months of Hajj and then performs Hajj for themselves in the same year, it is permissible, and they are considered to be performing Tamattu', provided they have already performed Umrah for themselves previously.

2. Performing Umrah for Oneself and Then Hajj for Someone Else:
   If a person performs Umrah for themselves during the months of Hajj and then performs Hajj on behalf of someone else in the same year, it is permissible, and they are considered to be performing Tamattu', provided they have already performed Hajj for themselves previously.

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Conclusion:

There is no issue with a person performing Umrah on behalf of someone else and then performing Hajj for themselves, or performing Umrah for themselves and then Hajj on behalf of someone else in the same year, as long as they have already completed both Umrah and Hajj for themselves.

Hajj and Umrah are obligatory only once in a lifetime, and any additional performance is voluntary and Sunnah.

By adhering to these conditions, it becomes clear that combining Umrah on behalf of another person and Hajj for oneself in the same year is permissible.