Let us suppose that there does exist another part of reality that would match up with what is currently referred to as "Heaven", which I shall consider to be a location for the existence of dead people in some sort of afterlife.
I will set aside what kind of "Heaven" we are discussing due to the seemingly limitless versions being promoted throughout history to include the gloomy afterlife of the ancient Greeks, the Summerland of the Spiritualists, the multiple Bardo states of the Tibetan Buddhists, the seven heavens of many shamanistic religions, the Cube City in the sky fundamentalist Christian version (which has always reminded me of the Borg from Star Trek), etc.
Let's just assume that by "Heaven" we mean some kind of afterlife location in which dead people can continue to exist for a certain period of time (finite or infinite, depending on the version chosen).
Now let's suppose that it is scientifically proven to be real. (Please. All of you who are gagging. Get a grip!)
So how would an extended life - an afterlife - affect the suffering and hope of the world's people, as you now ask?
Not at all.
What?
Not at all??!Yep.
Please understand that the vast majority of the human population already do believe in an afterlife.
And yet their behavior remains identical with regard to how they live their lives to those fewer in number who do not believe.
You see, your real question I would suggest is how would knowledge of an afterlife change how people would behave.
And beneath
that question, you are asking an even deeper question which is how would the ethics of people be different if they possessed a knowledge of an afterlife.
Any set of ethical principles are based on that person's values.
Understand that the only difference between the values of someone who assumes they will live only about 75 years on average (if they stop tailgating cars on the freeways and do not get struck down by disease) and the values of someone who fully expects to continue living after death (Get a grip, people!) is quantity of life not quality of life.
Let's pull away from "Heaven" a moment to make this easier to discuss.
Let us suppose that Aubrey de Grey succeeds with his SENS project and some people become functionally immortal. (Or Michael West at Bio-Time accomplishes the same goal with his approach. Or someone else).
(We substitute extended life on earth for an extended life after death in "Heaven").
Now exactly how will the reality of knowing that you could extend your life as an unending youthful, vigorous human being affect your "suffering in this world"?
Well if your fear of death is your primary source of your "suffering" then having a likely stay of execution would have a very profound and powerful effect on you.
But the simple fact of the matter is that most people do not "suffer" because they fear death. They
value death. The often view death as an escape hatch from other "suffering" such as having to work at a job, having physical ailments, having a lousy love life, irritating in-laws or neighbors, and overall seeing life as a zero sum game that they are always losing.
You can personally check this out to your heart's content by simply asking people a question: "If you could physically live forever, healthy and youthful, would you want to?"
If you ask this question I assure you that over 99% of the people you ask will tell you "NO!"
Check it for yourself.
Then think about what this means.
In my humble opinion it simply points to the fact that most people hate their lives.
Another simple test of this is to stand on a bridge over a busy freeway on Monday morning during rush hour. Count the number of happy, smiling faces you see ...if you see any at all.
So if an extended life were offered to these people I would suggest that at this point in history most of them would turn it down.
Now back to "Heaven".
If "Heaven" is a place where you can extend your life, obviously most people wouldn't really want it anyway unless it was radically different in a positive way from their lives right now.
And here is the stinger.
They do not have the slightest idea as to how it would really need to be different except to say that it would need to be without the problems they have.
They cannot tell you what they want that is different.
They can only tell you what they want to
avoid.
They want to avoid working hard, feeling lousy, being lonely, having irritating people around them, on and on.
So to these poor sick people, "Heaven" is the absence of what they do not like - but damned if they know what they
do want.
Well, I'll tell you what they want.
In a word.
Happiness.
They want lasting happiness.
But they do not believe that that is possible!
If you doubt me try to find the stories, the plays, the films that depict lasting happiness for the characters in them.
Shakespeare's comedies are where everyone gets married at the end of the play.
Shakespeare's tragedies are where everyone dies after they get married!

In fairy tales and ghost stories the third wish is for death.
The examples are endless, historical and cross-cultural.
But the key to happiness is to
choose to be happy.
That's it.
Notice what you like and indulge yourself.
If worry stops you from happiness then do something about it if you can and then indulge yourself in what you do like.
Create the habit of happiness.
Then you can stop worrying about "Heaven" and have a Hell of good time whether there is an afterlife or not.
Just my opinion.