How should one legally handle the pension of a mother suffering from asthma, which amounts to 74,000 Algerian Dinars, given that her son has performed Hajj and Umrah on her behalf, and she has other children living separately from her?

The pension that devolved to your mother after your father's death, if it was a grant from the state to the deceased's wife and minor children, then it belongs to them. If the mother loses the capacity to act, the authority to manage it transfers to her guardian to spend on her from it in a way that is most beneficial to her, and he is not permitted to donate any part of it.

However, if the pension was entitlements due to your father from the state or his employer, then it is an inheritance that is to be divided among all heirs according to Islamic law, and your mother's share is to be managed by her guardian.