Is it permissible to supplicate for someone if they request the supplication for their deceased father on their behalf?

It is permissible to supplicate for a person with prayers that include the good of this world and the Hereafter without seeking their permission, just as the Prophet, peace and blessings be upon him, supplicated for 'Umar and the mother of Abu Hurayrah. Combining supplication for him and for his parents is better.