Is it permissible to accept money that my mother promised me after high school, knowing that she did not give my older sister such money, and would this be considered favoritism? And if it is not permissible, how can I ask my sister for permission without causing her embarrassment?

It is obligatory to be equitable among children in giving gifts, and it is not permissible to favor some over others except for a need. If the mother prefers one of her children, she must either return the gift or give the others an equivalent amount. Favoritism is permissible if it is due to a need, such as a reward for success or for study expenses, and the mother did not possess what she could give to the others. There is no harm in asking the siblings for their forgiveness in this matter.