Can the saying "May the soul forgive you in this world and the hereafter" lead to a person being forgiven in the hereafter, knowing that everyone will receive what is due to them and desires good deeds for salvation?

Forgiving rights means relinquishing them in this world and the hereafter, seeking Allah's reward. This is better than delaying the taking of one's due until the Day of Judgment. Forgiveness is the benevolent act of friends and the righteous, and it is superior to triumphing and exacting one's right, especially if the wronged person is capable of taking their due. In this case, forgiveness is a higher degree than forgiveness when one is unable to act.