Is it permissible to give money saved for Hajj to one's father so that he may perform Hajj with it, while postponing one's personal Hajj to a later year, and will the doer be rewarded, and what is the ruling if the one who gave the money passes away before performing his obligatory Hajj?

As long as you are able to perform Hajj and have secured its expenses, you must perform Hajj immediately, for Allah Almighty says: ﴿And ˹due˺ to Allah from the people is a pilgrimage to the House—for whoever can find a way to it. And whoever disbelieves—then indeed, Allah is free from need of the worlds.﴾ [Aal-Imran: 97], and for the Prophet’s (peace be upon him) saying: «Whoever intends to perform Hajj, let him hasten to it, for one may fall ill, lose his mount, or face a pressing need.»

If you subsequently manage to secure the expenses for Hajj, you should give them to your father so he can perform the Hajj pilgrimage. If you cannot secure them alone, then you and your siblings should strive to gather the Hajj expenses for your father.