Here is the character sketch of the postmaster in Dhumketu's short story:
We first hear from the postmaster when he can be heard asking the clerk about Coachman Ali. The clerk calls out Ali's name in jest and tells the postmaster that Ali has been coming to the post office everyday for the last five years. (Each day, Ali faithfully hopes for a letter from his only daughter, Miriam.) The postmaster wants to know why Ali keeps coming as he never gets any letters. He scoffs at Ali's child-like patience and naivety:
"Who does he think will have time to write a letter every day?"
So, we can see that, initially, the postmaster is not very sympathetic towards Ali. When the clerk assures him that Ali 'is a bit touched,' he muses
"It seems as though the mad live in a world of their own making. To them, perhaps, we too appear mad. The mad-man's world is rather like the poet's, I should think!"
He really thinks Ali's imagination has gotten the better of him. One day, he finds himself becoming very impatient with Ali; while he is in a hurry to leave for some time off in the country, Ali detains him for some last minute instructions regarding his daughter, Miriam's letter. The postmaster loses his temper and barks at Ali:
"Have you no sense?" he cried. "Get away!"
"Do you think we're going to eat your letter when it comes?" and he walked off hastily.
After that day, Ali was never seen again. However, one day, the postmaster finds himself in the same predicament. His own daughter is ill in another town, and he is anxiously waiting for word from her. Rifling through the post, he comes across a letter that he thinks is from his daughter. Surprisingly, it is for Ali. He is shocked and asks Lakshmi Das, the clerk, where Ali is. The clerk does not know and says he will find out. The postmaster himself spends a troubled night waiting for word from his daughter. He suddenly realizes the depth of sorrow, grief and worry a parent experiences when there is no word from his child as to her whereabouts, her safety, or her health. Resolved to be kinder to Ali, he decides that he will give Miriam's letter to Ali himself. At five in the morning, Ali finally appears. However, the otherworldly light in Ali's eyes renders the postmaster speechless.
He is is further shaken when the clerk informs him that Ali has been dead for three months. Later, he and the clerk walk to Ali's grave to deliver Miriam's letter. He is now thoroughly chastened regarding his earlier and frequently insensitive impatience towards Ali when Ali was alive. He now sees the 'essential human worth of a letter' :
But the postmaster now watched them as eagerly as though each contained a warm, beating heart. He no longer thought of them in terms of envelopes and postcards.
As he settles down for another night of restless waiting for news of his sick daughter, he is 'tortured by doubt and remorse' for his past unkind treatment of Ali.
Hope this helps. Thanks for the question.