Perhaps the more predominate of the two opinions of the Fuqaha (that of the Hanafi and Hanbali schools) is that any action you perform with the intention of gifting the reward to that person, any person, will benefit them (whether they are alive or dead).

This is evidenced by numerous hadith in which the Sahabah asked the Messenger about performing acts (Hajj, Sadaqah, Sawm, etc) on behalf of other people and he permitted them.

Additionally, He – Alaihi al-Salam- mentioned that “When one of you dies his actions are cut off, except for three…” meaning his statements and physical actions are no longer existent, but that the reward from others actions carried on because of you are continuous “… perpetual charity, or beneficial knowledge, or a righteous child supplicating for you.”

For the living, if a group of people share in a sacrificial animal, yet only one of them physically sacrifices it, they will all be rewarded. For Udhiyyah, the Messenger sacrificed two large rams, the first saying at sacrfice “This is for Muhammad and the family of Muhammad” and for the second “This is for the Ummah of Muhammad.” Narrated by Ahmad in the Musnad.

So in short, gifting the reward of any good deed you do with the intention of benefiting someone else will benefit them. However, if you have not made Hajj for yourself, you must make Hajj for yourself first, then you can make Hajj for anyone else you wish.
And Allah knows best.