According to Buddhist theory, it's possible that dead beings can sense their relatives who are still alive. I referred a little bit about to this yesterday, that people who have recently died may be in a sensitive kind of realm in which they are still attached and still viewing us. They may be disturbed if their relatives are sad, crying, "I want you back, I want you back! And feel pulled back but can't return. But if we wish them well, "Go, travel on peacefully. Now your life is somewhere else," or similar good thoughts of wishing them well, it will help them more easily to go on their way.
Ever felt homesick? You wanted to be home but you were not. Well, a similar feeling supposedly happens when a person dies. They can be homesick. But if they have been wished well, and if they are being sent good wishes of, "Ok, go ahead, it's ok.", then they may feel better and make it easier for them to go on to their next life. Those are the benefits that can come to the loved one, by us wishing them well after they died.
There are also benefits for us and others. If we reflect on their good qualities and if we feel it helps them, it also helps us be less focused on what we have lost and more focused on continuing to help them. Which will enable us to have less grief. And if we encourage others to think of the person's goodness that may help to cheer them, as well.