Disclaimer: Not mine.
There will be sunlight.
There will be a whole world of light and shadows; there will be day and night, stars and clouds and cool whispering breezes. The timelessness of Azkaban, the sense of stagnancy within its cold stone walls, will fade to distant memory, and there will be sunlight again.
Someday, they will realize their mistake. Dumbledore will wake one morning and know the truth; Remus will come to his defense; the Ministry will let him go.
He will stagger from the prison, will laugh as he passes through the gate, as he escapes the Dementors. He will laugh defiantly, euphoric with freedom and relief, and he will taste the sunlight.
Remus will be waiting, a little older, a little grayer, and there will be a deep remorse in his gentle eyes. Sirius will forgive his friend, and everything will be just as it used to be.
They'll find Harry, and raise him as their own. They'll teach him about his parents, tell him stories about how James tried to win Lily for years before she finally gave in. Harry will smile, so like his father, so like his mother, a perfect mix of both.
And there will be days full of sunlight and laughter, days spent recapturing lost time, days spent in love and friendship.
There will be sunlight, when he is free.