Do the parents and the giver of charity get rewarded when giving charity to an orphaned sister with the intention of giving charity on behalf of the deceased mother, and is this considered an act of upholding kinship ties for them? And do the parents and the giver of charity get rewarded when honoring a guest or relatives with food or a gift with the intention of giving charity on behalf of the deceased mother, and is this considered an act of upholding kinship ties for them, especially if the honoring is for relatives?

Giving charity to relatives and honoring them with food with the intention of it being a charity on behalf of the mother is correct, and the doer will be rewarded for it. It is an act of filial piety towards the mother and a way of maintaining kinship ties, based on the Prophet's (peace and blessings be upon him) saying: "Is there any act of filial piety left for me to do for my parents after their death?" He replied: "Yes, four things: supplicating for them, seeking forgiveness for them, fulfilling their promises, honoring their friends, and maintaining the ties of kinship which you have only through them." And his (peace and blessings be upon him) saying: "Your charity to a relative is both charity and maintaining kinship ties."