[The Ruling on Performing Two Ḥajj in One Year on Behalf of a Deceased Person]

Answer—and Allah grants success: There is, as it appears to me, no objection to that. If two persons perform two Hajj for a single man, that is valid. What is prohibited is for a single person to perform two Hajj in one year—whether for himself or for someone else. It is valid for a single person to enter iḥrām for Hajj and ʿUmrah together in one iḥrām.
The Hajj legislated in the Sharīʿah is of three types:
1. Entering iḥrām for Hajj alone.
2. Entering iḥrām for ʿUmrah, then enjoying it up to Hajj (tamattuʿ).
3. Entering iḥrām for Hajj and ʿUmrah together.
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1