Answer
Wa`alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Yes, someone else can pay for your Hajj. As long as you fulfill all the required conditions and perform all the essential rites, your Hajj is valid in Islam—even if fully or partially sponsored. What matters is fulfilling the obligation correctly, not who pays.
In this regard, the Standing Committee for Islamic Research and Ifta’ in Saudi Arabia issued the following fatwa:
The validity of your Hajj is not affected by the fact that you have not spent any of your own money on it, or that you only spent a little and someone else paid most of the expenses of your Hajj.
Therefore, if your Hajj fulfilled the conditions and you did all the essential parts of Hajj, then you have fulfilled the obligation of Hajj, even if someone else covered the expenses.
Allah Almighty knows best.
Excerpted with modifications from: www.islamqa.info