Because of its unique essence, and considering its degree of existence, this world is a mix of happiness and sorrow, joy and grief, and hardship and ease. You can never find total bliss and happiness in it. Some of the hardships people may have in it are actually divine tests so that the believing can be distinguished from the rest.
As for true welfare and happiness, it can only be found in the hereafter, and it only belongs to the righteous and believing, and is obtained through effort and action in this world. This world serves as a prelude to the next.
Of course if what you mean by happiness and welfare are the blessings of this world such as wealth and high positions and ranks, it must be said that yes, it is possible for one to have these and at the same time secure happiness and bliss in the hereafter as well, given that he is a pious believer; a good example of such, would be Prophet Suleyman (pbuh).
The nature and existential essence of this world is in a way that no one living in it, kafir or mu’min, is free from sorrow and pain; even the wealthiest may suffer from problems that the poor may never experience. The reason for all this being that this world is a world of interference and clash between things, pain, hardship, restriction and transience. This leads to it being a mix of the causes of tragedy, pain, illness, hardship, defeat, and the causes of success, victory, happiness, joy and welfare. Thus, you can never find anyone in it who enjoys total bliss and happiness and never suffers from any hardship at all, just like you can never find anyone who suffers from total misery without experiencing any happiness. There are many wealthy people who at first sight may seem to enjoy perfect lives without any problems, while as a matter fact may suffer from mental, physical, psychological, or family related issues.
Allah (swt) has designed this world in a way that it remains a means of testing for man at all times, so that the good can be separated from the bad.
At the same time, in many cases, hardship and defeat are preludes to relief and success, and tragedies lead to the awakening of people, wiping out all signs of ignorance and forgetfulness and entailing the remembrance of the Lord. Allah (swt) says in the Quran: “Certainly We afflicted Pharaoh's clan with droughts and loss of produce, so that they may take admonition”.
All of this being said, true and lasting prosperity, pleasure and happiness can only be found in the hereafter and belonging to the pious mu’minin at that. Of course this world is the bridge to the next, and the only way to secure salvation and prosperity there is through acting and making an effort in this world. Therefore, this world not only is devoid of negative value, but bears positive value, like the hereafter.
To conclude, true happiness and joy (that is not tainted with any hardship and sorrow) can only be found in the next life, so it doesn’t make sense to say that one can have true happiness in this world and the next; true happiness belongs to the pious believers in the next life only.
But if what is meant by happiness and welfare, is relative happiness, which is to enjoy the blessings of this life, such as wealth and high positions, then one can have it in both this life and the next, given that he is a pious believer; a good example for this being Prophet Suleyman (pbuh).