Is it permissible for the grandmother to give some money to the questioner's mother from her monthly salary after the death of the grandmother's husband, or is the money still considered the deceased husband's money?

What your grandmother inherited from her husband is her property, and she has the right to dispose of it through gifts and similar means. There is no blame upon her if she gifts her daughter (your mother) whatever she wishes from it, provided that she treats all her children equally in giving, if she has children other than your mother.